Initial-to-Interface Maps for the Heat Equation on Composite Domains
Natalie E. Sheils, Bernard Deconinck · Studies in Applied Mathematics · 2016
A map from the initial conditions to the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with n interfaces. The existence of this map allows changing the problem at hand from an interface problem to a boundary value problem which allows for an alternative to the approach of finding a closed-form solution to the interface problem.