Sufficient condition for logarithmic nonlinearity in nonlinear evolution equations

Abstract

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.