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Finite speed of propagation and asymptotic rates for some nonlinear higher order parabolic equations with absorption*

Published online by Cambridge University Press:  14 November 2011

F. Bernis
F. Bernis
Affiliation:
Departamento de Matemáticas, Universidad Politécnica de Cataluńa, Apdo. 30002, 08034 Barcelona, Spain
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Synopsis

The “energy solutions” to the equation

have finite speed of propagation if l < q < 2 or l < r < 2. If 1 <r <2 (Vq <1) support u(· t) is uniformly bounded for t >0 (localisation property) and if q<2 ≦ r, sharp upper bounds of the interface (or free boundary) are obtained. We use a weighted energy method, the weights being powers of the distance to a variable half-space. We also study decay rates as t→∞ and extinction in finite time for bounded and unbounded domains (with null Dirichlet boundary conditions). Our equation includes the porous media equation with absorption. Analogous results hold if (−Δ)m is replaced by an appropriate quasilinear elliptic operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 104 , Issue 1-2 , 1986 , pp. 1 - 19
Copyright
Copyright © Royal Society of Edinburgh 1986

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