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Asymptotic stability and blowup of solutions for a class of viscoelastic inverse problem with boundary feedback
Author(s) -
Shahrouzi Mohammad
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.3646
Subject(s) - mathematics , overdetermination , viscoelasticity , stability (learning theory) , mathematical analysis , relaxation (psychology) , exponential stability , inverse , boundary (topology) , nonlinear system , class (philosophy) , infinity , boundary value problem , zero (linguistics) , inverse problem , function (biology) , geometry , psychology , social psychology , philosophy , linguistics , physics , epistemology , quantum mechanics , machine learning , artificial intelligence , evolutionary biology , biology , computer science , thermodynamics
In this paper, we consider a nonlinear viscoelastic inverse problem with memory in the boundary. Under some suitable conditions on the coefficients, relaxation function, and initial data, we proved stability of solutions when the integral overdetermination tends to zero as time goes to infinity. Furthermore, we show that there are solutions under some conditions on initial data that blow up in finite time. Copyright © 2015 John Wiley & Sons, Ltd.