Construction of a blow-up solution for a complex nonlinear heat equation

We construct a solution to a complex nonlinear heat equation which blows up in nite time T only at one blow-up point. We also give a sharp description of its blow-up pro le. The proof relies on the reduction of the problem to a nite dimensional one and the use of index theory to conclude. We note th...

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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 Taylor & Francis 01.04.2015
Subjects
Analysis of PDEs
Mathematics
Complex heat equation
Simultaneous blow-up
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Summary:We construct a solution to a complex nonlinear heat equation which blows up in nite time T only at one blow-up point. We also give a sharp description of its blow-up pro le. The proof relies on the reduction of the problem to a nite 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.
ISSN:0360-5302
1532-4133