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Blow-up profiles of solutions for the exponential reaction-diffusion equation (1102.4158v1)
Published 21 Feb 2011 in math.AP
Abstract: We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up profile. Our aim is to find the final time blow-up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach works also for the power nonlinearity.