Profile for a simultaneously blowing up solution for a complex valued semilinear heat equation

2013/06/19 by Nejla Nouaili, Nouaili, Nejla, Hatem Zaag +1
Engineering · Mathematics · #35B44 #35K40 #35K57 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1306.4435

openalex publication_date 2013/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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