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Title: Propagation versus constancy of support in the degenerate parabolic equation $u_t=f(u)\Delta u$
Authors: Winkler, Michael
Keywords: Degenerate diffusionsupport evolution
Issue Date: 2004
Publisher: Università degli Studi di Trieste. Dipartimento di Matematica e Informatica
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
36 (2004)
Abstract: A weak solution concept for the Dirichlet problem in bounded domains for the degenerate parabolic equation $u_t = f(u)\Delta u$ is presented. It is shown that if $\int_0^1 \frac{ds}{f(s)}<\infty$ then each nontrivial nonnegative weak solution eventually becomes positive, while if $\int_0^1 \frac{ds}{f(s)} = \infty$ then all weak solutions have their support constant in time.
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.36 (2004)

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