The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity | Zendy

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The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity

Author(s) -

Menglan Liao

Publication year - 2021

Publication title -

evolution equations and control theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.665

H-Index - 19

eISSN - 2163-2480

pISSN - 2163-2472

DOI - 10.3934/eect.2021025

Subject(s) - logarithm , complement (music) , mathematics , viscoelasticity , physics , nonlinear system , mathematical physics , mathematical analysis , thermodynamics , quantum mechanics , chemistry , biochemistry , complementation , gene , phenotype

This paper deals with the following viscoelastic wave equation with a strong damping and logarithmic nonlinearity:\begin{document}$ u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds-\Delta u_t = |u|^{p-2}u\ln|u|. $\end{document}A finite time blow-up result is proved for high initial energy. Meanwhile, the lifespan of the weak solution is discussed. The present results in this paper complement and improve the previous work that is obtained by Ha and Park [ Adv. Differ. Equ. , (2020) 2020: 235].

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