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Large Time Behavior and Stability of Equilibria of Degenerate Parabolic Equations

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Abstract

The article deals with positive solutions of the Dirichlet problem for

$$ u_{t} = f(u)(\Delta u + g(u)) \quad in \Omega \times (0,\infty), $$

where f(s)>0 for s>0 and f(0)=0. The asymptotic behavior of solutions is discussed for a rather large class of g. For g regular near zero, stability properties of equilibria are investigated.

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  1. Department of Mathematics I, RWTH Aachen, 52056, Aachen, Germany

    Michael Winkler

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  1. Michael Winkler
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Winkler, M. Large Time Behavior and Stability of Equilibria of Degenerate Parabolic Equations. J Dyn Diff Equat 17, 331–351 (2005). https://doi.org/10.1007/s10884-005-3142-1

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  • DOI: https://doi.org/10.1007/s10884-005-3142-1

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