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On the blow-up results for a class of strongly perturbed semilinear heat equations

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  • We consider in this work some class of strongly perturbed for the semilinear heat equation with Sobolev sub-critical power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to derive the blow-up rate. We also classify all possible asymptotic behaviors of the solution when it approaches to singularity. Finally, we describe precisely the blow-up profiles corresponding to these behaviors.
    Mathematics Subject Classification: Primary: 35K58, 35K55; Secondary: 35B40, 35B44.

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