Sufficient condition for logarithmic nonlinearity in nonlinear evolution equations

摘要

In this paper, the author establishes a sufficient condition for logarithmic nonlinearity in nonlinear evolution equations. Lian et al. (Nonlinear Anal. 184, 2019, 239-257) proved the existence and blow-up of solution for the hyperbolic equations with logarithmic nonlinearity. However, there is a critical error in proving the local existence of the solutions. For this previous result to be correct, logarithmic nonlinearity needs additional conditions. We establish a sufficient condition for logarithmic nonlinearity in Lian et al. Moreover, we also give the condition of logarithmic nonlinearity to the parabolic equations.