Journal Article

Spatial decay in a cross-diffusion problem

L. E. Payne and J. C. Song

in IMA Journal of Applied Mathematics

Published on behalf of Institute of Mathematics and its Applications

Volume 72, issue 6, pages 854-864
Published in print December 2007 | ISSN: 0272-4960
Published online October 2007 | e-ISSN: 1464-3634 | DOI:
Spatial decay in a cross-diffusion problem

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In this paper, the authors investigate the decay of end effects for a cross-diffusion problem defined on a semi-infinite cylindrical region. With homogeneous Dirichlet or Neumann conditions prescribed on the lateral surface of the cylinder, it is shown that for fixed finite time and under certain restrictions on the coefficients, solutions decay point-wise as the distance d from the finite end of the cylinder tends to infinity at least of order ekd2. Under less restrictive conditions, it is shown that solutions decay in L2 at least as fast as ekd. In both cases, k is a computable function of time.

Keywords: cross-diffusive problem; spatial decay; energy bounds

Journal Article.  0 words. 

Subjects: Applied Mathematics

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