Nonlinear damped wave equation: Existence and blow-up

Nonlinear damped wave equation: Existence and blow-up

In this paper, we consider the following nonlinear wave equation with variable exponents: utt−Δu+aut|ut|m(⋅)−2=bu|u|p(⋅)−2,where a,b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents...

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Veröffentlicht in:Computers & mathematics with applications (1987) 2017-12, Vol.74 (12), p.3024-3041
Hauptverfasser: Messaoudi, Salim A., Talahmeh, Ala A., Al-Smail, Jamal H.
Format: Artikel
Sprache:eng
Schlagworte:
Blow up
Existence
Exponents
Finite element analysis
Galerkin method
Nonlinear damping
Nonlinear equations
Solutions
Variable nonlinearity
Wave equations
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Beschreibung
Zusammenfassung:In this paper, we consider the following nonlinear wave equation with variable exponents: utt−Δu+aut|ut|m(⋅)−2=bu|u|p(⋅)−2,where a,b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.07.048