The one-dimensional heat equation with a nonlocal initial condition

Abstract

A boundary value problem for the one-dimensional heat equation is considered under the constraint of a nonlocal initial condition. The problem is investigated by conversion to a Fredholm integral equation. The solution of the integral equation is derived as an eigenfunction expansion that is valid for situations in which either uniqueness or nonuniqueness applies. Circumstances under which a resonance effect occurs are discussed and illustrated with an example.