Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity | Zendy

Wei Lian | Zendy; M.S. Ahmed | Zendy; Runzhang Xu | Zendy

Open Access

Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity

Author(s) -

Wei Lian,

M.S. Ahmed,

Runzhang Xu

Publication year - 2020

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2020.40.1.111

Subject(s) - mathematics , logarithm , nonlinear system , polynomial , product (mathematics) , mathematical analysis , wave equation , type (biology) , power (physics) , physics , geometry , quantum mechanics , biology , ecology

In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (E(0) < d, E(0) = d and E(0) > 0) using potential well method. The results in this article shed some light on using potential wells to classify the solutions of the semilinear wave equation with the product of polynomial and logarithmic nonlinearity.

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