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Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
Journal article   Open access  Peer reviewed

Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

Younes Bidi, Abderrahmane Beniani, Khaled Zennir and Ahmed Himadan
Demonstratio mathematica, Vol.54(1), pp.245-258
28/07/2021
DOI: https://doi.org/10.1515/dema-2021-0022

Abstract

35L20 35L70 35Q91 35R11 47G20 fractional Laplacian fractional Sobolev spaces global existence hyperbolic problem potential well
We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.
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https://doi.org/10.1515/dema-2021-0022View
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