On a nonlinear wave equation in unbounded domains (Q1108488)

Summary: We study existence and uniqueness of the nonlinear wave equation \[ \partial ^ 2u/\partial t^ 2+M(x,\int | \nabla u(x,t)| ^ 2 dx+\int | u(x,t)|^ 2 dx)(-\Delta u+u)= 0 \] in unbounded domains. The above model describes nonlinear wave phenomenon in non- homogeneous media. Our techniques involve fixed point arguments combined with the energy method.