A Remark on a Nonlocal-in-Time Heat Equation

Abstract

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.

Keywords

• Semilinear heat equation
• nonlocal in time
• existence of global solutions