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A Remark on a Nonlocal-in-Time Heat Equation
Christoph Walker1
1 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 825-831.

Schauder’s fixed point theorem is used to derive the existence of solutions to a semilinear heat equation. The equation features a nonlinear term that depends on the time-integral of the unknown on the whole, a priori given, interval of existence.

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DOI : 10.5802/crmath.443
Classification : 35K58
Mots clés : Semilinear heat equation, nonlocal in time, existence of global solutions
Christoph Walker 1

1 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Christoph Walker. A Remark on a Nonlocal-in-Time Heat Equation. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 825-831. doi : 10.5802/crmath.443. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.443/

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[8] Victor N. Starovoitov; Botagoz Syarovoitova Modeling the dynamics of polymer chains in water solution. Application to sensor design, J. Phys., Conf. Ser., Volume 894 (2017) no. 1, 012088

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