Journal of Applied Mathematics

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

Zhigang Pan, Hong Luo, and Tian Ma

Full-text: Open access

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 ) ) .

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 805158, 15 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495207

Digital Object Identifier
doi:10.1155/2012/805158

Mathematical Reviews number (MathSciNet)
MR2948142

Zentralblatt MATH identifier
1254.35050

Citation

Pan, Zhigang; Luo, Hong; Ma, Tian. Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms. J. Appl. Math. 2012 (2012), Article ID 805158, 15 pages. doi:10.1155/2012/805158. https://projecteuclid.org/euclid.jam/1355495207


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