Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

Zhigang Pan, Hong Luo and Tian Ma

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt − kΔut = f(x, Δu) + g(x, u, Du, D2u) in a bounded and smooth domain Ω in Rn, where f(x, Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g(x, u, Du, D2u) is in a sense subordinated to f(x, Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution u∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).

Date: 2012
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https://doi.org/10.1155/2012/805158

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:805158

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