About an initial-boundary value problem from magneto-hydronamics.
Gerhard Ströhmer (1992)
Mathematische Zeitschrift
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Gerhard Ströhmer (1992)
Mathematische Zeitschrift
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K. Gröger, J. Rehberg (1993)
Mathematische Zeitschrift
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M. Alfaro, D. Hilhorst (2010)
Mathematical Modelling of Natural Phenomena
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In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.
Jakub Staněk, Josef Štěpán (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Kouachi, Said (2002)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Wei-Ming Ni (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
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....
Salah Badraoui (1999)
Applicationes Mathematicae
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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.