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, 1-15

Abstract:

We consider the global existence of strong solution u , corresponding to a class of fully nonlinear wave equations with strongly damped terms u t t - k Δ u t = f ( x , Δ u ) + g ( x , u , D u , D 2 u ) in a bounded and smooth domain Ω in R n , where f ( x , Δ u ) is a given monotone in Δ u nonlinearity satisfying some dissipativity and growth restrictions and g ( x , u , D u , D 2 u ) is in a sense subordinated to f ( x , Δ u ) . By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution u ∈ L l o c ∞ ( ( 0 , ∞ ) , W 2 , p ( Ω ) ∩ W 0 1 , p ( Ω ) ) .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:805158

DOI: 10.1155/2012/805158

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