Type: Article

Periodic problem for the nonlinear damped wave equation with convective nonlinearity

Carreño-Bolaños, R.; Juárez-Campos B.; Naumkin, Pavel I.;

Abstract:

We study the nonlinear damped wave equation with a linear pumping and a convective nonlinearity. We consider the solutions, which satisfy the periodic boundary conditions. Our aim is to prove global existence of solutions to the periodic problem for the nonlinear damped wave equation by applying the energy-type estimates and estimates for the Green operator. Moreover, we study the asymptotic profile of global solutions.