Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation

We construct a solution to a complex nonlinear heat equation which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude. We no...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 40; no. 7; pp. 1197 - 1217
Main Authors Nouaili, Nejla, Zaag, Hatem
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 03.07.2015
Taylor & Francis Ltd
Taylor & Francis
Subjects
Analysis of PDEs
Blowing
Brownian motion
Complex heat equation
Construction
Heat equations
Markov analysis
Mathematical analysis
Mathematics
Nonlinearity
Partial differential equations
Proving
Reduction
Simultaneous blow-up
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Summary:We construct a solution to a complex nonlinear heat equation which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude. We note that the real and imaginary parts of the constructed solution blow up simultaneously, with the imaginary part dominated by the real.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2015.1018997