Luisa Consiglieri

Independent Researcher · Mathematics

This paper investigates the existence of weak solutions to two problems set of elliptic equations in adjoining domains, with Beavers--Joseph--Saffman and regularized Butler--Volmer boundary conditions being prescribed on the common interfaces, porous-fluid and membrane, respectively. Mathematically, the modeling tool is the coupled Stokes/Darcy pro...

We model the operative treatment of incompetent truncal veins using endovenous laser ablation (EVLA). Three differential equations, namely the diffusion, the heat and the bioheat equations, are considered in the endovenous-perivenous multidomain, describing the lumen, the vein wall, the tissue pad and the skin. Exact solutions are provided. Our mai...

The heat conducting compressible viscous flows are governed by the Navier–Stokes–Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat transfer at the boundary. On one part of the boundary, we consider the Navier slip boundary condition, while in the remaining part the inlet and outlet o...

The heat conducting compressible viscous flows are governed by the Navier-Stokes-Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat transfer at the boundary. On one part of the boundary, we consider the Navier slip boundary condition, while in the remaining part the inlet and outlet o...

Presentation in: 2nd International Conference on the Teaching of Mathematics (at the undergraduate level) University of Crete, Hersonissos, Greece, July 1-6, 2002.

This paper investigates the existence of weak solutions of biquasilinear boundary value problem for a coupled elliptic-parabolic system of divergence form with discontinuous leading coefficients. The mathematical framework addressed in the article considers the presence of an additional nonlinearity in the model which reflects the radiative thermal...

This paper deals with thermoelectric problems including the Peltier and Seebeck effects. The coupled elliptic and doubly quasilinear parabolic equations for the electric and heat currents are stated, respectively, accomplished with power-type boundary conditions that describe the thermal radiative effects. To verify the existence of weak solutions...

In the presence that most books are either too mathematical or too physical, this book is written with the belief that mathematical methods should be communicated to a wider audience than just mathematicians. It offers new physical models and new mathematical approaches that are disperse throughout the research journals in the last years. The physi...

There are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at...

Coupled mathematical models for the radiofrequency (RF) ablation performed in biomedical sciences have been developed based on the bioheat transfer theory. The heat exchange problem is important to be analytically studied in order to control the size of the necrosis zone caused by RF ablation. This lesion size in the tissue may be predicted by the...

A mathematical model of nonlinear radiation is introduced into a thermoelectrochemical problem, and its qualitative analysis is focused on existence of solutions. The main objective is the nonconstant character of each parameter, that is, the coefficients are assumed to be depend on the spatial variable and the temperature. Making recourse of known...

We investigate the regularity in $L^p$ ($p>2$) of the gradient of any weak solution of a Cauchy problem with mixed Neumann-power type boundary conditions. Under suitable assumptions we prove the existence of weak solutions that satisfy explicit estimates. Some considerations on the steady-state regularity are discussed.

We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We investigate explicit estimates for solutions of the parabolic equations with nonhomogeneous boundary condition...

We deal with the existence of quantitative estimates for solutions of mixed problems to an elliptic second order equation in divergence form with discontinuous coefficient. Our concern is to estimate the solutions with explicit constants, for domains in $\mathbb{R}^n$ ($n\geq 2$) of class $C^{0,1}$. The existence of $L^\infty$ and $W^{1,q}$-estimat...

The architecture has its basis in a dialectic search of new choices of representation. We deal with the form on the contemporary architecture under two approaches: expression and content. We examine how mathematical principles based on natural growth can be applied in architectural design in order to create a dynamic, rather than static, structure....

There are two main directions in this paper. One is to find sufficient conditions to ensure the existence of weak solutions to thermoelectric problems. At the steady-state, these problems consist by a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least on a nonempty...

We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real applications. Our objective is the derivation of explicit expressions of the involved constants in the quantitative...

Catheter ablation along the posterior aspect of the left atrium has a small but real risk of esophageal perforation. This left atrioesophageal fistula formation is associated with multiple gaseous and/or septic embolic events causing cerebral and myocardial damage. The main objective is to mathematically model the ablation associated with delivery...

We examine the complete coupled thermoelectrochemical system that describes reaction problems. The cross effects, namely the thermoelectric (Peltier-Seebeck), the thermodiffusion (Dufour-Soret), and the electrochemical diffusion, occur as reciprocal phenomena of irreversible processes. We deal with convective/radiative heat-transfer boundary condit...

A Stokesian fluid in motion along a porous medium saturated by the same fluid is modelled by the Beavers—Joseph—Saffman boundary-value problem to generalized Forchheimer—Stokes—Fourier systems: what we call the Beavers—Joseph—Saffman (BJS) problem. The model has nonlinear character given by the temperature dependence of physical parameters such as...

A new model is introduced for describing the heat-conducting viscous fluids over porous media. The innovative features of the presented model are the nonlinear character given by temperature dependence of the physical parameters such as the viscosities, the permeability, and complementary the thermal conductivity and thermal expansion. The flow vel...

We examine the important role played by perfusion-mediated tissue cooling due to large vessels during the radio-frequency ablation procedures performed in biomedical sciences. The existence of blood flow near heated tissue carries away the heat from the ablation zone. This undesired thermal dissipation, known as the cooling effect, affects the fina...

We prove the global solvability of an initial boundary value problem for the Stokes-Fourier system when the thermal expansion makes a nonincompressibility behavior. The natural convection including Oberbeck-Boussinesq effects appears as its primordial application. The solutions are obtained as limits of the so-called Faedo-Galerkin approximations,...

The work deals with the coupled system constituted by the equations of motion and energy with nonlinear and nonlocal boundary conditions in order to describe the thermal flow motion of a class of non-Newtonian fluids and the convective-radiation balance, respectively. For the constitutive laws in an n-dimensional space (n = 2,3), the stress tensor...

Two boundary value problems for an elliptic equation in divergence form with bounded discontinuous coefficient are studied in a bidomain. On the interface, generalized dynamic boundary conditions such as of the Wentzell-type and Signorini-type transmission are considered in a subdifferential form. Several non-constant coefficients and nonlinearitie...

A complete study of heat conducting viscous flows presents several nonlinearities: the convections, the Joule effect and energy dependent conductivity and viscosities. Adopting the general thermodynamics process, the constitutive relations for the Cauchy stress tensor and the heat flux are nonlinear with p and q coercivity parameters, respectively,...

Considering a mixed boundary-value problem for a non-linear heat equation with the non-homogeneous Neumann condition, the right-hand side and the initial condition in space of sign-measures, we establish large-data existence results even if the convective term is not integrable. In order to develop a theory under minimal assumptions on given data,...

We deal with the transmembrane sodium diffusion in a nerve. We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions. This system of partia...

The stationary Oseen equations are studied in R3 in its general form, that is, with a non-constant divergenceless function on the convective term. We prove existence, uniqueness and regularity results in weighted Sobolev spaces. From this new ap- proach, we also state existence, uniqueness and regularity results for the generalized Oseen model whic...

The Boussinesq approximation to the Fourier-Navier-Stokes flows under the elec- tromagnetic field is considered. Such a model is the so-called Maxwell-Boussinesq approximation. We proposed the new approachto the problem. We prove the exis- tence and uniqueness of weak solutions to the variational formulation of the model. Some further regularity in...

This work deals with generalized viscous flows that can only undergo isochoric motions in isothermal processes, but can sustain motions that are not necessarily isochoric in processes that are not isothermal. The heat-conducting Stokes and Bingham fluids appear as a direct application. The method used here is a combination of a fixed point argument...

Continuity as the mathematical tool in the creation of architectural forms is known as morphocontinuity. In the present work, we explain how morphocontinuity appears on the work of Eero Saarinen and discuss its correspondence with its environmental (physical, social and cultural) contexts. Keywords: Eero Saarinen; mappings; transformations

We investigate the nonlinear coupled system of elliptic partial differential equations which describes the fluid motion and the energy transfer what we call the ( p - q) coupled fluid-energy system due to p and q coercivity parameters correlated to the motion and heat fluxes, respectively. Due to the simultaneous action of the convective-radiation...

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with...

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary conditions. The partial regularity for the velocity of the fluid is proved to each proper weak solution, tha...

We prove the existence and uniqueness of weak solutions to the variational formulation of the Maxwell-Boussinesq approximation problem. Some further regularity in $W^{1,2+\delta}$, $\delta>0$, is obtained for the weak solutions. The shape sensitivity analysis by the boundary variations technique is performed for the weak solutions. As a result, the...

The existence of proper weak solutions of the Dirichlet-Cauchy problem constituted by the Navier-Stokes-Fourier system which characterizes the incompressible homogeneous Newtonian fluids under thermal effects is studied. We call proper weak solutions such weak solutions that verify some local energy inequalities in analogy with the suitable weak so...

We study different boundary value problems to the p(x)-Laplacean equation, namely of Robin and Signorini types. We prove the existence and uniqueness of weak solutions to the problems under study and also their continuous dependence on the exponent data.

The threefold interest in architecture, biology and mathematics motivated us to examine and justify new architectural forms. We discuss some notions of rhythm: Euclidean, morphogenetic and morphologic. Contemporary relationships between structure and form are based on the generation of shape by technological processes, thus the resulting objects ar...

The threefold interest in architecture, biology and mathematics motivated us to examine and justify new architectural forms. We discuss some notions of rhythm: Euclidean, morphogenetic and morphologic. Contemporary relationships between structure and form are based on the generation of shape by technological processes, thus the resulting objects ar...

A model for the ergometer rowing exercise is presented in this paper. From the quantitative observations of a particular trajectory (motion), the model is used to determine the moment of the forces produced by the muscles about each joint. These forces are evaluated according to the continuous system of equations of motion. An inverse dynamics anal...

The transmission of an electric current in a conductor is a process in which some electrical energy is converted into heat (thermal energy). We deal with a nonlinear boundary value elliptic problem which describes the electrical heating of a solid conductor and the Joule-Thomson effect is taken into account. The existence of a weak solution is prov...

abstract: We recall and solve the equivalence problem for a flat C connection ∇ in Euclidean space, with methods from the theory of differential equations. The problem consists in finding an affine transformation of R^n taking ∇ to the so called trivial connection. Generalized solutions are found in dimension 1 and some exam-ple problems are solved in d...

We prove the existence of strong 2-dimensional solutions for two Cauchy-Dirichlet problems to the Navier-Stokes-Fourier system which characterizes the Newtonian fluids under heat-conducting effects. The nonstationary Navier-Stokes system for an incompressible homogeneous fluid with temperature dependent viscosity is completed by the equation of bal...

This work adresses an unsteady heat flow problem involving friction and convective heat transfer behaviors on a part of the boundary. The problem is constituted by a variational motion inequality with energy dependent coefficients, and the energy equation in the framework of L 1-theory for the dissipative term. Using the duality theory of convex an...

Related publication: L. CONSIGLIERI and V. CONSIGLIERI, Continuity versus discretization. Nexus Network Journal 11 :2 (2009), 151--162. DOI: 10.1007/s00004-008-0086-x

We state an abstract variational formulation to a coupled system consisted by an inequality and an equality motivated by the motion and energy equations, and the constitutive laws for the stress tensor and the heat flux, respectively, when non-Newtonian fluids are taken care of. Here the existence of a weak solution is proven via a fixed point argu...

The knowledge of the nerve impulse in medicine is of particular rele- vance to the improvement of medical diagnostic and therapeutic methods. The electrochemical behaviour of the axon membrane plays an important and key role in the resulting nerve impulse, which can be related to the movement of ions between the extra and intracellular regions due...

Apresenta-se nesta comunicação um modelo matemático para a análise do movimento humano. Este modelo baseia-se na dinâmica multi-corpos por forma a compreender a trajectória e a coordenação dos momentos internos das forças. A abordagem utilizada para estabelecer um sistema acoplado de equações diferenciais de movimento consiste em introduzir o deslo...

RELATED PUBLICATIONS: L. CONSIGLIERI and E.B. PIRES, Um modelo analítico para a determinação de momentos internos utilizando dinâmica multi-corpos inversa, in Proceedings of Métodos Numéricos e Computacionais em Engenharia CMNE CILAMCE 2007 Eds. J. César de Sá, R. Delgado, A.D. Santos, A. Rodríguez-Ferran, J. Oliver, P.R.M. Lyra and J.L.D. Alves, A...

We investigate the nonlinear coupled system of elliptic partial differential equations which describes the fluid motion and the energy transfer, due to the simultaneous action of the convective-radiation effects on a part of the boundary,

We consider Bingham incompressible flows with temperature dependent viscosity and plasticity threshold and with mixed boundary conditions, including a friction type boundary condition. The coupled system of motion and energy steady-state equations may be formulated through a variational inequality for the velocity and variational methods provide a...

A mathematical model for the analysis of human motion is presented in this paper. This model is based on linkage dynamics in order to understand trajectory and internal moment of force coordination. Mobility at the base of the supporting limb is a critical factor in the freedom to fall forward. The approach used to state a coupled system of differe...

We consider unsteady flows of a homogeneous incompressible fluid-like material with the viscosity depending on the temperature and on the shear-rate, and the heat conductivity being a function of the temperature and its gradient. Restricting to the internal flows and assuming Navier's slip at the tangential directions on the boundary, we establish...

Seminar in: NEČAS SEMINAR ON CONTINUUM MECHANICS, organized by the Mathematical Institute of the Charles University, Necas Center for Mathematical Modeling, Prague, Czech Republic, October 2, 2006. Séminaire de Mathématiques et de leurs applications, Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de L’Adour, Pau, France, D...

The images in architecture are handed down through mathematical forms. The meaning of the plastic value of the forms and the conflict between their visual boundaries are a result of the geometrical composition of the object. Since Stonehenge in Britain, the Egyptian pyramids, the Greek Parthenon or the Roman Pantheon, architecture has been a reflex...

We deal with a coupled system of elliptic motion and energy equations motivated by the thermal flow of a class of non-Newtonian fluids. A nonlocal Coulomb friction condition on a part of the liquid-solid boundary is taken into account. On this part of the boundary it is also considered a convective-radiative heat transfer related to the frictional...

Thermal viscous incompressible flows present several nonlinearities: the convections, the viscous heating, the conductivity and viscosities dependence on the internal energy, and the constitutive laws for the stress tensor and the heat flux when non-Newtonian fluids are taken care of. In the present work, different friction laws are considered on a...

A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn–Hilliard equation coupled with a system describing a class of non-Newtonian incompressible fluid with p-structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p⩾ 2 and for...

In the present work we deal with a problem motivated by the solid and/or fluid thermomechanics, and we establish an existence result of a weak solution. For a n-dimensional bounded domain (n>1) with a sufficiently smooth boundary constituted by two disjoint complementary open subsets, we study an elliptic boundary value problem. The (p-q) structure...

We deal with a coupled system of elliptic motion and energy equations motivated by the thermal flow of a class of non-Newtonian fluids. A nonlocal Coulomb friction condition on a part of the liquid-solid boundary is taken into account. On this part of the boundary it is also considered a convective-radiative heat transfer related to the frictional...

We deal with a variational inequality describing the motion of incompressible fluids, whose viscous stress tensors belong to the subdifferential of a functional at the point given by the symmetric part of the velocity gradient, with a nonlocal friction condition on a part of the boundary obtained by a generalized mollification of the stresses. We e...

We discuss the mathematical modeling of incompressible viscous flows for which the viscosity depends on the total dissipation energy. In the two-dimensional periodic case, we begin with the case of temperature-dependent viscosities with very large thermal conductivity in the heat convective equation, in which we obtain the Navier-Stokes system coup...

RELATED PUBLICATIONS: L. CONSIGLIERI and J.F. RODRIGUES, Steady-state Bingham flow with temperature dependent nonlocal parameters and friction, in Free Boundary Problems: Theory and Applications Ed. I.N. Figueiredo, J.F. Rodrigues and L. Santos, Intern. Series Numerical Math. 154 Birkhauser Verlag, Switzerland 2007, 149--157. L. CONSIGLIERI, J.F...

A nonlocal constitutive law for an incompressible viscous flow in which the viscosity depends on the total dissipation energy of the fluid is obtained as the limit case of very large thermal conductivity when the viscosity varies with the temperature. A rigorous analysis is illustrated within the Hilbertian framework for unidirectional stationary f...

Thermal ablative therapies have been increasingly used to treat malignant tumors in liver, kidney, lung and bone tissues. Among those therapies radio-frequency ablation has become the most world widely used thermal therapy to treat liver cancer. During RF ablation, a thin electrode is placed directly into the tumor using ultrasound, computed tomogr...

Thermal ablative therapies have been increasingly used to treat malignant tumors in liver, kidney, lung and bone tissues. Among those therapies radio- frequency ablation has become the most world widely used thermal therapy to treat liver cancer. During RF ablation, a thin electrode is placed directly into the tumor using ultrasound, computed tomog...

The ground reaction force and the center of pressure are very important measurements in clinical and rehabilitation settings to predict internal moments generated at the hip, knee and ankle during the process of patient assessment. Explicit equations for a jumping model are stated, and the present mathematical model can be extended for gait models....

RELATED PUBLICATION: L. CONSIGLIERI, The squat jumping model revisited, in Proceedings of Encontro 1, Biomecânica Eds. J.A. Simões, H.C. Rodrigues, M.A. Vaz and A.P. Veloso (2005), 231--234. https://www.researchgate.net/publication/282851304_The_squat_jumping_model_revisited

Ablative therapies such as radio-frequency (RF) ablation are increasingly used for treatment of tumours in liver and other organs. Often large vessels limit the extent of the thermal lesion, and cancer cells close to the vessel survive resulting in local tumour recurrence. Accurate estimates of the heat convection coefficient h for large vessels wi...

In this paper, we prove regularity results for weak solutions to some stationary problems arising in the theory of generalized Newtonian fluids with energy transfer. Namely, we prove that these solutions are strong. In the two-dimensional case, we prove the Hlder continuity of the first gradient of a solution. Bibliography: 30 titles.

Proposing a one-year mathematics course for architecture students, the aim of this work is to examine the relevance of mathematics in contemporary architecture, namely its most representative forms of cultural or sport buildings. Because today the architectural object is characterized by a great exuberance, some notions of topology are required; cl...

We present a coupled system of elliptic equations describing the steady state of the thermoelectrical behaviour of an aluminium electrolytic cell. The thermal model is a free boundary problem which consists of the heat equation with Joule heating as a source. We neglect the Joule heating in the ledge, and allow for temperature-dependent electrical...

In this work we study the flow for a class of non-Newtonian fluids with a nonlocal friction condition obtained by the mollification of the normal stresses on part of the boundary. Considering a reformulated problem using an abstract boundary operator, we prove an existence result for the steady case. The mathematical framework of the paper is mainl...

As everybody knows, mathematics has been the basis of all sciences. Specially, engineering, medicine, applied sciences such as physics, chemistry, biology and so on. It is also known that mathematics has always accompanied or, at least, tried to follow arts in their diversities, codes, geometrical signs, harmony and proporcionality researches. The...

We prove an existence result for a coupled system of partial differential equations, valid for dimensions two and three. To prove this mathematical result, we use a fixed point argument for multivalued mappings. The main part of this work is to obtain estimates in the presence of L 1 -data and to prove continuous dependence with respect to given pa...

In the present paper, we shall consider a nonlinear thermoconvection problem consisting of a coupled system of nonlinear partial differential equations due to temperature dependent coefficients. We prove that weak solutions exist in appropriate Sobolev spaces under mild hypothesis on the regularity of the data. This result is established through a...

We prove the existence of weak solutions to the coupled system of stationary equations for a class of general non-Newtonian fluids with energy transfer. In particular, we may include Bingham flows that lead to classical free boundary problems of fluid dynamics. Using convex analysis and L1-theory for elliptic mixed boundary value problems, we consi...

A p-Laplacian flow (1 < p < ∞) with nonlocal diffusivity is obtained as an asymptotic limit case of a high thermal conductivity flow described by a coupled system involving the dissipation energy. Keywordsnon-Newtonian fluids–asymptotic limits–nonlocal models

The stationary Oseen equations are studied in $\mathbb R^3$ in its general form, that is, with a non-constant divergenceless function on the convective term. We prove existence, uniqueness and regularity results in weighted Sobolev spaces. From this new approach, we also state existence, uniqueness and regularity results for the generalized Oseen m...