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Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions


Authors: Jonas Haehnle and Andreas Prohl
Journal: Math. Comp. 79 (2010), 189-208
MSC (2000): Primary 35K55, 65M12, 65M15
DOI: https://doi.org/10.1090/S0025-5718-09-02231-5
Published electronically: July 1, 2009
MathSciNet review: 2552223
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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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Additional Information

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: https://doi.org/10.1090/S0025-5718-09-02231-5
Received by editor(s): December 19, 2007
Received by editor(s) in revised form: July 23, 2008
Published electronically: July 1, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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