Wave equations with super-critical interior and boundary nonlinearities

Lorena Bociu, Mohammad Rammaha and Daniel Toundykov

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 6, 1017-1029

Abstract: This article presents a unified overview of the latest, to date, results on boundary value problems for wave equations with super-critical nonlinear sources on both the interior and the boundary of a bounded domain Ω∈Rn. The presented theorems include Hadamard local wellposedness, global existence, blow-up and non-existence theorems, as well as estimates on the uniform energy dissipation rates for the appropriate classes of solutions.

Keywords: Wave; Super-critical source; Nonlinear damping; Existence; Uniqueness; Energy decay (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:6:p:1017-1029

DOI: 10.1016/j.matcom.2011.04.006

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