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Intrinsic decay rate estimates for abstract wave equation with memory
Author(s) -
Hao Jianghao,
Wei Jing
Publication year - 2017
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.4375
Subject(s) - dissipative system , mathematics , ode , convex function , viscoelasticity , function (biology) , kernel (algebra) , mathematical analysis , wave equation , regular polygon , nonlinear system , mathematical physics , pure mathematics , physics , quantum mechanics , thermodynamics , geometry , evolutionary biology , biology
In this paper, we consider an abstract wave equation in the presence of memory. The viscoelastic kernel g ( t ) is subject to a general assumptiong ′ ( t ) ⩽ − H ( g ( t ) ) , where the function H (·)∈ C 1 ( R + ) is positive, increasing and convex with H (0)=0. We give the decay result as a solution to a given nonlinear dissipative ODE governed by the function H ( s ). Copyright © 2017 John Wiley & Sons, Ltd.