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Asymptotic stability and blow up of solutions for a Petrovsky inverse source problem with dissipative boundary condition
Author(s) -
Tahamtani F.,
Shahrouzi M.
Publication year - 2012
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.2629
Subject(s) - mathematics , dissipative system , inverse , dissipation , exponential stability , constraint (computer aided design) , boundary (topology) , mathematical analysis , stability (learning theory) , infinity , boundary value problem , inverse problem , geometry , physics , nonlinear system , computer science , quantum mechanics , machine learning , thermodynamics
This paper is concerned with global in time behavior of solutions for a quasilinear Petrovsky inverse source problem with boundary dissipation. We establish a stability result when the integral constraint vanishes as time goes to infinity. We also show that the smooth solutions blow up when the data is chosen appropriately. Copyright © 2012 John Wiley & Sons, Ltd.