Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity

By Wei-Cheng Lian, Md Salik Ahmed, Runzhang Xu. Nonlinear Analysis, 2016

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In this paper we consider the semi-linear wave equation with logarithmic nonlinearity. By modifying and using potential well combined with Sobolev inequality, we gain the results of global existence and blow up at infinity of solution at all initial energy level. The results in this article guide that the polynomial nonlinearity is a critical condition of blow up in finite time for the semi-linear wave equation.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/17db47b74abc1f01123b827e4c004ec6e5ab2f79