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On the decay and blow‐up of solution for coupled nonlinear wave equations with nonlinear damping and source terms
Author(s) -
Hao Jianghao,
Wang Fei
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4181
Subject(s) - nonlinear system , mathematics , polynomial , mathematical analysis , work (physics) , energy (signal processing) , function (biology) , boundary value problem , exponential function , wave equation , energy method , initial value problem , exponential decay , physics , statistics , quantum mechanics , evolutionary biology , biology , thermodynamics , nuclear physics
In this work, we consider a nonlinear coupled wave equations with initial‐boundary value conditions and nonlinear damping and source terms. Under suitable assumptions on the damping terms and source terms and initial data in the stable set, we obtain that the decay estimates of the energy function is exponential or polynomial by using Nakao's method. By using the energy method, we obtain the blow‐up result of solution with some positive or nonpositive initial energy. Copyright © 2016 John Wiley & Sons, Ltd.