Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations | Zendy

Faramarz Tahamtani | Zendy; Amir Peyravi | Zendy

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Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations

Author(s) -

Faramarz Tahamtani,

Amir Peyravi

Publication year - 2013

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1212-15

Subject(s) - viscoelasticity , mathematics , relaxation (psychology) , exponential growth , exponential function , energy (signal processing) , mathematical analysis , nonlinear system , boundary value problem , exponential decay , initial value problem , physics , thermodynamics , statistics , quantum mechanics , psychology , social psychology , nuclear physics

In this paper, we study the initial-boundary value problem for a system of nonlinear viscoelastic Petrovsky equations. Introducing suitable perturbed energy functionals and using the potential well method we prove uniform decay of solution energy under some restrictions on the initial data and the relaxation functions. Moreover, we establish a growth result for certain solutions with positive initial energy.

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