Asymptotic stability and blow up of solutions for a Petrovsky inverse source problem with dissipative boundary condition | Zendy

Tahamtani F. | Zendy; Shahrouzi M. | Zendy

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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.

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