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Publications (10)
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion, proliferation, and saturation. First, the behavior of the solution is analyzed by numerical simulations, and it is discus...
In this paper, we analyze the asymptotic profiles of zero points with respect to the spatial variable of the solutions to the heat equation in one-dimensional space. By giving suitable conditions of the initial data, we prove the existence of a zero point such that the asymptotic behavior is $O(t)$ as $t\to+\infty$ and its coefficient is characteri...
A Correction to this paper has been published https://doi.org/10.1007/s00285-020-01534-6
A new method to derive an essential integral kernel from any given reaction–diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called “effective equation” including the reduced integral kernel (called “effective ker...
![Fig 3. Original model and its reduction. (a) The original model ([19],...](publication/347684881/figure/fig3/AS:986261259030529@1612154416297/Original-model-and-its-reduction-a-The-original-model-19-Eqs-1-and-2-The_Q320.jpg)
Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteris...
In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on...
A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective ker...
![Fig 3. Model reduction. The original model ( [19], equations (1, 2))...](publication/342443821/figure/fig1/AS:906323315142657@1593095725473/Model-reduction-The-original-model-19-equations-1-2-considered-a-band-like_Q320.jpg)
Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteris...
In this paper, we study the existence of traveling wave solutions connecting two constant states to a nonlocal scalar equation with sign-changing kernel. A typical example of such kernel in the neural fields is the Mexican hat type function. We first introduce a new notion of upper-lower-solution for the equation of wave profile for a given wave sp...
