Open AccessExistence and decay of solution to coupled system of viscoelastic wave equations with strong damping in Rn
Author(s) -
Keltoum Bouhali,
Fateh Ellaggoune
Publication year - 2021
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.41175
Subject(s) - sobolev space , viscoelasticity , galerkin method , forcing (mathematics) , nonlinear system , energy method , mathematical analysis , mathematics , function (biology) , wave equation , energy (signal processing) , physics , thermodynamics , quantum mechanics , statistics , evolutionary biology , biology
In this paper, we establish a general decay rate properties of solutions for a coupled system of viscoelastic wave equations in IRn under some assumptions on g1; g2 and linear forcing terms. We exploit a density function to introduce weighted spaces for solutions and using an appropriate perturbed energy method. The questions of global existence in the nonlinear cases is also proved in Sobolev spaces using the well known Galerkin method.