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Strong solutions to a nonlocal-in-time semilinear heat equation. (English) Zbl 1461.35131

Summary: The 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.

MSC:

35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35R09 Integro-partial differential equations
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