Global existence and blow-up of solutions to a semilinear heat equation with logarithmic nonlinearity

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.

Keywords:

• Semilinear heat equation
• logarithmic nonlinearity
• global existence
• blow-up

MSC:

• 35B40
• 35K35
• 35K58

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.

Additional information

Funding

The research has been supported by NSFC – National Natural Science Foundation of China [grant number 11201380].