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Journal of Applied Mathematics
Volume 2005, Issue 3, Pages 219-233

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 Hindawi Publishing Corporation. 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.


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 uM(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.