Functional solutions for problems of heat and mass transfer

TL;DR

This paper investigates the existence and uniqueness of functional solutions to boundary value problems in PDE systems related to heat and mass transfer, exploring conditions under which these solutions coincide with classical solutions.

Contribution

It establishes conditions for the existence and uniqueness of functional solutions and compares them with classical solutions in heat and mass transfer PDE problems.

Findings

Proves existence of functional solutions for certain PDE boundary value problems.

Identifies conditions where functional and classical solutions are equivalent.

Provides simple cases where solution sets coincide.

Abstract

We prove the existence and, in certain cases, the uniqueness of functional solutions for two boundary value problems of systems of P.D.E. in divergence form motivated by problems of heat and mass transfer. If $\cc_F$ and $\cc$ denote respectively the set of functional and classical solutions of these problems we settle, in simple cases, the question if $\cc_F=\cc$.