Refined asymptotics for the blowup of ut — δu = up

Stathis Filippas; Robert V. Kohn

doi:10.1002/cpa.3160450703

Refined asymptotics for the blowup of u_t — δu = u^p

Stathis Filippas, Robert V. Kohn

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This work is concerned with positive, blowing‐up solutions of the semilinear heat equation u_t — δu = u^p in Rⁿ. Our main contribution is a sort of center manifold analysis for the equation in similarity variables, leading to refined asymptotics for u in a backward space‐time parabola near any blowup point. We also explore a connection between the asymptotics of u and the local geometry of the blowup set.

Original language	English (US)
Pages (from-to)	821-869
Number of pages	49
Journal	Communications on Pure and Applied Mathematics
Volume	45
Issue number	7
DOIs	https://doi.org/10.1002/cpa.3160450703
State	Published - Aug 1992

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.3160450703

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abstract = "This work is concerned with positive, blowing‐up solutions of the semilinear heat equation ut — δu = up in Rn. Our main contribution is a sort of center manifold analysis for the equation in similarity variables, leading to refined asymptotics for u in a backward space‐time parabola near any blowup point. We also explore a connection between the asymptotics of u and the local geometry of the blowup set.",

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Refined asymptotics for the blowup of u_t — δu = u^p

Abstract

ASJC Scopus subject areas

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