A Remark on a Nonlocal-in-Time Heat Equation
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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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.443/ |
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| author | Walker, Christoph |
| author_facet | Walker, Christoph |
| author_sort | Walker, Christoph |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-23677f4c5804412d8ef57e705ecd223a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-23677f4c5804412d8ef57e705ecd223a2025-02-07T11:07:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-05-01361G482583110.5802/crmath.44310.5802/crmath.443A Remark on a Nonlocal-in-Time Heat EquationWalker, Christoph0Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, GermanySchauder’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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.443/Semilinear heat equationnonlocal in timeexistence of global solutions |
| spellingShingle | Walker, Christoph A Remark on a Nonlocal-in-Time Heat Equation Comptes Rendus. Mathématique Semilinear heat equation nonlocal in time existence of global solutions |
| title | A Remark on a Nonlocal-in-Time Heat Equation |
| title_full | A Remark on a Nonlocal-in-Time Heat Equation |
| title_fullStr | A Remark on a Nonlocal-in-Time Heat Equation |
| title_full_unstemmed | A Remark on a Nonlocal-in-Time Heat Equation |
| title_short | A Remark on a Nonlocal-in-Time Heat Equation |
| title_sort | remark on a nonlocal in time heat equation |
| topic | Semilinear heat equation nonlocal in time existence of global solutions |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.443/ |
| work_keys_str_mv | AT walkerchristoph aremarkonanonlocalintimeheatequation AT walkerchristoph remarkonanonlocalintimeheatequation |