Strong Solutions to a Nonlocal-in-Time Semilinear Heat Equation

Christoph Walker

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arXiv · 2007.05029

Strong Solutions to a Nonlocal-in-Time Semilinear Heat Equation

Christoph Walker

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Abstract

Existence of strong solutions to a nonlocal semilinear heat equation is shown. The main feature of the equation is that the nonlocal term depends on the unknown on the whole time interval of existence, the latter being given a priori. The proof relies on Schauder's fixed point theorem and semigroup theory.

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Christoph Walker. 2020-07-09. Strong Solutions to a Nonlocal-in-Time Semilinear Heat Equation. https://arxiv.org/abs/2007.05029

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