Carreño-Bolaños, Rafael; Juarez-Campos, Beatriz; Naumkin, Pavel I. Periodic problem for the nonlinear damped wave equation with convective nonlinearity. (English) Zbl 1452.35103 Stud. Appl. Math. 145, No. 1, 137-149 (2020). Summary: 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. Cited in 3 Documents MSC: 35L71 Second-order semilinear hyperbolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs 35B45 A priori estimates in context of PDEs Keywords:asymptotics of solutions; linear pumping; periodic boundary conditions; energy-type estimates; estimates of the Green operator PDFBibTeX XMLCite \textit{R. Carreño-Bolaños} et al., Stud. Appl. Math. 145, No. 1, 137--149 (2020; Zbl 1452.35103) Full Text: DOI