Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation | Zendy

Nadjat Doudi | Zendy; Salah Boulaaras | Zendy; Nadia Mezouar | Zendy; Rashid Jan | Zendy

Open Access

Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation

Author(s) -

Nadjat Doudi,

Salah Boulaaras,

Nadia Mezouar,

Rashid Jan

Publication year - 2022

Publication title -

discrete and continuous dynamical systems - s

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 34

eISSN - 1937-1632

pISSN - 1937-1179

DOI - 10.3934/dcdss.2022106

Subject(s) - dissipation , logarithm , term (time) , mathematical analysis , wave equation , mathematics , boundary (topology) , nonlinear system , physics , boundary value problem , quantum mechanics

In this paper, we consider a wave equation with logarithmic source term and fractional boundary dissipation. We study the global existence of the solution under some conditions and prove the general decay of the solution in this case by using the Lyapunov functional. Also, the blow-up of solution is established at three different levels of energy using the potential well method.

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