ABSTRACT
In this paper, we study the initial boundary value problem of a semilinear heat equation with logarithmic nonlinearity. By using potential well method and energy method, we obtain the existence of global solutions and finite-time blow-up solutions. Moreover, the upper bound of blow-up time is discussed under suitable assumptions.
Acknowledgments
The authors would like to thank the reviewers for their valuable comments and suggestions, which improve the initial version of the paper significantly.
Disclosure statement
No potential conflict of interest was reported by the authors.