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Adaptive FEM for reaction—diffusion equations
Applied Numerical Mathematics, 1998In the first part of the paper the author shortly presents some methods for solving mixed systems of nonlinear parabolic and elliptic differential equations. Especially a short comparison between the adaptive method of lines and Rothe's approach is presented. Then the author describes the time integrator and the finite element method (FEM) derived from
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Nonlocal Reaction-diffusion Equations
2014We introduced nonlocal reaction-diffusion equations in Section 2.4 of Chapter 1 by means of the model of competition of species. It is also possible to view them in a different way. If individuals of some population consume resources in some area around their average position, then we need to take into account this nonlocal consumption of resources in ...
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Exact Solutions of Reaction-Diffusion Equation
Journal of the Physical Society of Japan, 1993Summary: The statitical interactions of anyons on a plane are described by a gauge field. We present a natural periodic generalization of such gauge field and find that this agrees with the corresponding gauge field on a torus which has been obtained from the Chern-Simons theory.
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Reaction - diffusion equations in perforated media
Nonlinearity, 1997The author considers the problem \[ {\partial\over\partial t} u(t,x)= {1\over 2} \sum^r_{i,j= 1} a_{ij}(x){\partial^2\over \partial x_i\partial x_j} u(t,x)+ \sum^r_{i= 1} b_i(x){\partial\over\partial x_i} u(t,x),\;t\in (0,\infty),\;x\in D= \mathbb{R}^r\setminus \bigcup^\infty_{i= 1} H_i, \] \[ {\partial u\over\partial n}+ f(x,u)= 0,\;x\in\bigcup ...
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