Journal of Applied Mathematics 
Volume 2005 (2005), Issue 3, Pages 219-233
doi:10.1155/JAM.2005.219

On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms

E. Cabanillas Lapa, Z. Huaringa Segura, and F. Leon Barboza

 Instituto de Investigación, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Peru
Received 18 July 2004; Revised 9 March 2005

Abstract

We prove existence and uniform stability of strong solutions to a quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of the type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω.