A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 580-590
  • ISSN: 0023-5954

Abstract

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This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion system includes only a simple reaction and linear diffusion. Resolving semilinear problems is typically easier than dealing with nonlinear diffusion problems. Therefore, our ideas are expected to reveal new and more effective approaches to the study of nonlinear problems.

How to cite

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Murakawa, Hideki. "A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems." Kybernetika 45.4 (2009): 580-590. <http://eudml.org/doc/37722>.

@article{Murakawa2009,
abstract = {This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion system includes only a simple reaction and linear diffusion. Resolving semilinear problems is typically easier than dealing with nonlinear diffusion problems. Therefore, our ideas are expected to reveal new and more effective approaches to the study of nonlinear problems.},
author = {Murakawa, Hideki},
journal = {Kybernetika},
keywords = {reaction-diffusion system approximation; degenerate parabolic problem; cross-diffusion system; cross-diffusion system; Stefan problem; porous medium equation},
language = {eng},
number = {4},
pages = {580-590},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems},
url = {http://eudml.org/doc/37722},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Murakawa, Hideki
TI - A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 580
EP - 590
AB - This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion system includes only a simple reaction and linear diffusion. Resolving semilinear problems is typically easier than dealing with nonlinear diffusion problems. Therefore, our ideas are expected to reveal new and more effective approaches to the study of nonlinear problems.
LA - eng
KW - reaction-diffusion system approximation; degenerate parabolic problem; cross-diffusion system; cross-diffusion system; Stefan problem; porous medium equation
UR - http://eudml.org/doc/37722
ER -

References

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