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.