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General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms
Author(s) -
Pişkin Erhan,
Ekinci Fatma
Publication year - 2019
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.5429
Subject(s) - degenerate energy levels , bounded function , mathematics , viscoelasticity , relaxation (psychology) , mathematical analysis , domain (mathematical analysis) , type (biology) , work (physics) , energy method , nonlinear system , physics , quantum mechanics , psychology , social psychology , ecology , biology , thermodynamics
In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions g i ( i = 1,2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow‐up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature.