Age-dependent equations with non-linear diffusion

Christoph Walker

doi:10.3934/dcds.2010.26.691

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2010, Volume 26, Issue 2: 691-712. Doi: 10.3934/dcds.2010.26.691

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Age-dependent equations with non-linear diffusion

Christoph Walker^1,

1.
Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D–30167 Hannover

Received: October 2008

Revised: April 2009

Published: July 2010

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Abstract

We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend non-linearly and possibly non-locally on the density itself. The abstract approach is applied to concrete examples.

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Mathematics Subject Classification: Primary: 35M10, 35K90; Secondary: 92D25.

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