Approximation of singularly perturbed parabolic reaction-diffusion equations with nonsmooth data.
Shishkin, G. I. (2001)
Computational Methods in Applied Mathematics
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Shishkin, G. I. (2001)
Computational Methods in Applied Mathematics
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V. Dinakar, N. Barani Balan, K. Balachandran (2017)
Nonautonomous Dynamical Systems
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We consider the reaction-diffusion equation with discontinuities in the diffusion coefficient and the potential term. We start by deriving the Carleman estimate for the discontinuous reaction-diffusion operator which is deployed in the inverse problems of finding the stability result of the two discontinuous coefficients from the internal observations of the given parabolic equation.
Beyn, W.-J., Kolezhuk, V.S., Pilyugin, S.Yu. (2004)
Zapiski Nauchnykh Seminarov POMI
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Hideki Murakawa (2009)
Kybernetika
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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....
Bizhanova, G.I. (2004)
Zapiski Nauchnykh Seminarov POMI
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Liljana Stefanovska, Toma Grcev, Sonja Gegovska-Zajkova (2002)
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Xavier Cabré, Joana Terra (2009)
Journal of the European Mathematical Society
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Viera Paulíny-Tothová (1966)
Matematicko-fyzikálny časopis
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