Mathematics of Computation

Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions

Author(s): Jonas Haehnle; Andreas Prohl.
Journal: Math. Comp. 79 (2010), 189-208.
MSC (2000): Primary 35K55, 65M12, 65M15
Posted: July 1, 2009
Retrieve article in: PDF

Abstract: Weak solutions for nonlinear wave equations involving the $p(\mathbf{x})$ -Laplacian, for $p: \Omega \rightarrow (1,\infty)$ are constructed as appropriate limits of solutions of an implicit finite element discretization of the problem. A simple fixed-point scheme with appropriate stopping criteria is proposed to conclude convergence for all discretization, regularization, perturbation, and stopping parameters tending to zero. Computational experiments are included to motivate interesting dynamics, such as blowup, and asymptotic decay behavior.

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Retrieve articles in Mathematics of Computation with MSC (2000): 35K55, 65M12, 65M15

Jonas Haehnle
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: haehnle@na.uni-tuebingen.de

Andreas Prohl
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: prohl@na.uni-tuebingen.de

DOI: 10.1090/S0025-5718-09-02231-5
PII: S 0025-5718(09)02231-5
Received by editor(s): December 19, 2007
Received by editor(s) in revised form: July 23, 2008
Posted: July 1, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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