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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Keywords: Semilinear heat equation, nonlocal in time, existence of global solutions
Christoph Walker 1
@article{CRMATH_2023__361_G4_825_0, author = {Christoph Walker}, title = {A {Remark} on a {Nonlocal-in-Time} {Heat} {Equation}}, journal = {Comptes Rendus. Math\'ematique}, pages = {825--831}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.443}, language = {en}, }
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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