Ansgar Jungel, Peter A. Markowich, & Giuseppe Toscani
Abstract:
Explicit decay rates for solutions of systems of degenerate parabolic
equations in the whole space or in bounded domains subject to
homogeneous Dirichlet boundary conditions are proven. These systems
include the scalar porous medium, fast diffusion and
p-Laplace equation and strongly coupled systems of these equations.
For the whole space problem, the (algebraic) decay rates turn out to be
optimal. In the case of bounded domains, algebraic and exponential decay
rates are shown to hold depending on the nonlinearities.
The proofs of these results rely on the use of the entropy
functional together with generalized Nash inequalities (for the whole
space problem) or Poincare inequalities (for the bounded domain case).
Published January 8, 2001.
Math Subject Classifications: 35K65, 35K55, 35B40.
Key Words: Explicit decay rates, long-time behavior of solutions,
algebraic decay, exponential decay, degenerate parabolic equations,
Nash inequality.
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Ansgar Jungel Fachbereich Mathematik und Statistik, Universit\"at Konstanz, 78457 Konstanz, Germany e-mail: juengel@fmi.uni-konstanz.de |
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Peter A. Markowich Institut f\"ur Mathematik Universitat Wien 1090 Wien, Austria e-mail: Peter.Markowich@univie.ac.at |
| Giuseppe Toscani Dipartimento di Matematica Universita di Pavia 27100 Pavia, Italy e-mail: toscani@dimat.unipv.it |
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