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A sharper decay rate for a viscoelastic wave equation with power nonlinearity
Author(s) -
Miyasita Tosiya,
Zennir Khaled
Publication year - 2020
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.5919
Subject(s) - mathematics , viscoelasticity , nonlinear system , mathematical analysis , a priori and a posteriori , contraction (grammar) , kernel (algebra) , galerkin method , a priori estimate , wave equation , regular polygon , geometry , physics , pure mathematics , medicine , philosophy , epistemology , quantum mechanics , thermodynamics
We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo‐Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex.