On a nonolinear wave equation in unbounded domains

Abstract

We study existence and uniqeness of the nonlinear wave equation∂2u∂t2+M(x,∫|∇u(x,t)|2dx+∫|u(x,t)|2dx)(−Δu+u)=0in unbounded domains. The above model describes nonlinear wave phenomenon in non-homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.