Refined asymptotics for the blowup of ut — δu = up

Stathis Filippas, Robert V. Kohn

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)821-869
Number of pages49
JournalCommunications on Pure and Applied Mathematics
Volume45
Issue number7
DOIs
StatePublished - 1992

Fingerprint

Blow-up
Semilinear Heat Equation
Parabola
Geometry
Center Manifold
Sort
Positive Solution
Space-time
Hot Temperature
Similarity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Refined asymptotics for the blowup of ut — δu = up . / Filippas, Stathis; Kohn, Robert V.

In: Communications on Pure and Applied Mathematics, Vol. 45, No. 7, 1992, p. 821-869.

Research output: Contribution to journalArticle

@article{6ed446f9e6bb48b9a05db407e1796325,
title = "Refined asymptotics for the blowup of ut — δu = up",
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.",
author = "Stathis Filippas and Kohn, {Robert V.}",
year = "1992",
doi = "10.1002/cpa.3160450703",
language = "English (US)",
volume = "45",
pages = "821--869",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "Wiley-Liss Inc.",
number = "7",

}

TY - JOUR

T1 - Refined asymptotics for the blowup of ut — δu = up

AU - Filippas, Stathis

AU - Kohn, Robert V.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990586490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990586490&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160450703

DO - 10.1002/cpa.3160450703

M3 - Article

VL - 45

SP - 821

EP - 869

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 7

ER -