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

Abstract

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.

50 pages

References in corpus (1)

• Construction of a stable blow-up solution for a class of strongly perturbed semilinear heat equations

Cited by in corpus (3)

• Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case
• The blow-up rate for a non-scaling invariant semilinear heat equation
• Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method