A blow-up problem for a nonlinear heat equation in the complex plane of time

Solutions of a nonlinear heat equation are numerically computed in the time variable t lying in the complex plane, and possible singularities are sought. It turns out that in the complex half plane { R [ t ] ≥ 0 } , where R denotes the real part of a complex number, there is no singularity other tha...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2016-02, Vol.33 (1), p.145-166
Main Authors: Cho, C.-H., Okamoto, H., Shōji, M.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
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Summary:Solutions of a nonlinear heat equation are numerically computed in the time variable t lying in the complex plane, and possible singularities are sought. It turns out that in the complex half plane { R [ t ] ≥ 0 } , where R denotes the real part of a complex number, there is no singularity other than that which exists on the real line. However, if we compute further in the Riemann surface, new singularities are found. A certain nonlinear Schrödinger equation which is associated with our problem is also computed numerically and we propose a conjecture that it is well-posed globally in time.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-015-0203-7