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

  • * Corresponding author: Jun Zhou

    * Corresponding author: Jun Zhou

The second author is supported by NSFC grant 11201380

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  • 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.

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

    Citation:

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