Some properties of strong solutions to nonlinear heat and moisture transport in multi-layer porous structures

TL;DR

This paper proves the existence of strong solutions for a complex system of nonlinear PDEs modeling heat and moisture transport in layered porous structures, using elliptic transmission problem regularity results.

Contribution

It establishes the existence of strong solutions to nonlinear heat and moisture transport equations in layered materials, a novel result in this context.

Findings

Existence of strong solutions in two dimensions for the model

Use of elliptic transmission problem regularity results

Mathematical validation of layered porous structure models

Abstract

The present paper deals with mathematical models of heat and moisture transport in layered building envelopes. The study of such processes generates a system of two doubly nonlinear evolution partial differential equations with appropriate initial and boundary conditions. The existence of the strong solution in two dimensions on a (short) time interval is proven. The proof rests on regularity results for elliptic transmission problem for isotropic composite-like materials.