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Periodic problem for the nonlinear damped wave equation with convective nonlinearity
Author(s) -
CarreñoBolaños Rafael,
JuarezCampos Beatriz,
Naumkin Pavel I.
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12316
Subject(s) - nonlinear system , mathematical analysis , mathematics , damped wave , convection , boundary value problem , wave equation , operator (biology) , energy (signal processing) , energy method , physics , mechanics , biochemistry , chemistry , statistics , repressor , quantum mechanics , transcription factor , gene
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.