Construction of a blow-up solution for a complex nonlinear heat equation.
Nouaili, Nejla; Zaag, Hatem (2015), Construction of a blow-up solution for a complex nonlinear heat equation., Communications in Partial Differential Equations, 40, 7, p. 1197-1217. 10.1080/03605302.2015.1018997
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Partial Differential Equations
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Abstract (EN)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.
Subjects / KeywordsComplex heat equation.; Simultaneous blow-up; Complex heat equation
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