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
Instituto de Investigación, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Peru
Received 18 July 2004; Revised 9 March 2005
Copyright © 2005 E. Cabanillas Lapa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.