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arXiv · 2208.14522

Blow up in a periodic semilinear heat equation

Marco Fasondini·John R. King·J. A. C. Weideman
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Abstract

Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel results include various asymptotic approximations that are, in combination, valid over the entire space and time interval right up to and including the blow-up time. Preliminary results on continuing a numerical solution beyond the singularity are also presented.

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Marco Fasondini, John R. King, J. A. C. Weideman. 2022-08-30. Blow up in a periodic semilinear heat equation. https://doi.org/10.1016/j.physd.2023.133660

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