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

摘要

We prove existence and uniform stability of strong solutions to aquasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity ofthe typeu″?M(∫Ω|?u|2dx)Δu+a(x)g(u′)+f(u)=0,inΩ×]0,+∞[,u=0,onΓ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), inΩ.