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Dynamics of a coupled system for nonlinear damped wave equations with variable exponents
Author(s) -
Zennir Khaled,
Miyasita Tosiya
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000094
Subject(s) - nonlinear system , viscoelasticity , constraint (computer aided design) , kernel (algebra) , dynamics (music) , wave equation , physics , variable (mathematics) , mathematical analysis , power (physics) , mathematics , classical mechanics , quantum mechanics , geometry , combinatorics , acoustics , thermodynamics
We consider a coupled system of viscoelastic wave equation with weak, strong damping and power nonlinearity. For a single viscoelastic wave equation, we have already obtained a global solution, its decay rate and finite‐time blow‐up [1]. In this paper, we extend these results to a coupled system. First, we obtain a global solution and derive its decay rate by a decreasing energy. Finally, we apply the concavity method in order to show that the solution blows up in finite time under nonclassic constraint on kernel functions.