Heat equation as a Friedrichs system

Inspired by recent advances in the theory of (Friedrichs) symmetric positive systems, we apply newly developed results to the heat equation, by showing how the intrinsic theory of Ern, Guermond and Caplain (2007) can be used in order to get a well-posedness result for the Dirichlet initial–boundary value problem. We also demonstrate the application of the two-field theory with partial coercivity of Ern and Guermond (2008), originally developed for elliptic problems, and also discuss different possibilities for the construction of the appropriate boundary operator.