Existence for a nonlinear wave equation with damping and source terms.
The paper deals with the Cauchy problem to the equation \(u_{tt}(t,x)-\triangle u(t,x)+Q(t,x,u_t)=f(x,u)\) with compactly supported initial data. The uniqueness and regularity of a solution are proved. The authors use Orlicz spaces and ingenious estimates, to obtain the results for a broad range of powers of the nonlinearities \(Q,f\).
scientific article; zbMATH DE number 2004888