Blowup solutions for the shadow limit model of singular Gierer-Meinhardt system with critical parameters

Abstract

We consider a nonlocal parabolic PDE, which may be regarded as the standard semilinear heat equation with power nonlinearity, where the nonlinear term is divided by some Sobolev norm of the solution. In this paper, we are interested in constructing blowup solutions under some critical regimes. We had a complete new phenomenon of the blowup speed with a log correction term.

arXiv comment40

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Cited by in corpus (1)

• Sharp equivalent for the blowup profile to the gradient of a solution to the semilinear heat equation