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

Xiumei Deng; Jun Zhou

doi:10.3934/cpaa.2020042

Article Contents

2020, Volume 19, Issue 2: 923-939. Doi: 10.3934/cpaa.2020042

This issue Previous Article Asymptotic profile of solutions to a certain chemotaxis system Next Article Global solvability and general decay of a transmission problem for kirchhoff-type wave equations with nonlinear damping and delay term

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

Xiumei Deng and
Jun Zhou^,

School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

^* Corresponding author: Jun Zhou
^* Corresponding author: Jun Zhou

Received: January 31, 2019

Revised: April 30, 2019

Published: October 2019

The second author is supported by NSFC grant 11201380

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Abstract

This paper concerns with a semilinear heat equation with singular potential and logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, the existence of global solutions and infinite time blow-up solutions are obtained. The results of this paper indicate that the polynomial nonlinearity is a critical condition of existence of finite time blow-up solutions to semilinear heat equation with singular potential.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35K58.

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