A new criterion for global existence or finite-time blow-up is obtained for the semilinear heat equation when the nonlinearity exponent lies between the Fujita and Sobolev critical values, via a similarity-transformed potential well approach.
Levine, Some nonexistence and instability theorems for solutions of formally parabolic equations of the formP u t =−Au+f(u), Arch
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On the existence and nonexistence of global solutions of the semilinear heat equation
A new criterion for global existence or finite-time blow-up is obtained for the semilinear heat equation when the nonlinearity exponent lies between the Fujita and Sobolev critical values, via a similarity-transformed potential well approach.