Abstract
Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jager and J. Kacur). In this paper the general variational formulation of the corresponding system is presented and its existence and convergence properties are verified; its application to one model problem (preserving the symmetry in the elliptic, but not in the parabolic part) is demonstrated.
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Vala, J. On a System of Equations of Evolution with a Non-Symmetrical Parabolic Part Occuring in the Analysis of Moisture and Heat Transfer in Porous Media. Applications of Mathematics 47, 187–214 (2002). https://doi.org/10.1023/A:1021741320045
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DOI: https://doi.org/10.1023/A:1021741320045