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

Nouaili, Nejla; Zaag, Hatem (2015), Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation, Communications in Partial Differential Equations, 40, 7, p. 1197-1217. 10.1080/03605302.2015.1018997

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1306.4435v4
Date
2015
Journal name
Communications in Partial Differential Equations
Volume
40
Number
7
Publisher
Marcel Dekker
Published in
Paris
Pages
1197-1217
Publication identifier
Metadata
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Author(s)
Nouaili, Nejla
Zaag, Hatem cc
Abstract (EN)
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.
Subjects / Keywords
Simultaneous blow-up; Complex heat equation