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Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. (English) Zbl 1479.35136

Summary: We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. In some earlier work [1], we constructed a blow-up solution for that equation, and showed that it blows up (at least) at the origin. We also derived the so called “intermediate blow-up profile”. In this paper, we prove the single point blow-up property and determine the final blow-up profile.

MSC:

35B44 Blow-up in context of PDEs
35K15 Initial value problems for second-order parabolic equations
35K58 Semilinear parabolic equations
35R09 Integro-partial differential equations
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