Displaying similar documents to “An Initial-Boundary-Value Problem for a Certain Density-Dependent Diffusion System.”

Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion

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.

Diffusion and cross-diffusion in pattern formation

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 2 × 2 systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.