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...
Saved in:
Published in | Communications in partial differential equations Vol. 40; no. 7; pp. 1197 - 1217 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Taylor & Francis Group
03.07.2015
Taylor & Francis Ltd Taylor & Francis |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |