On the analysis of an endothermal/exothermal saturation problem

In this paper we consider an endo or exo-thermal saturation problem that corresponds to a parabolic quasi-variational inequality. By using regularity results and inequalities of Lewy–Stampacchia type we prove the solvability of a modified problem (including the Steklov averaging and the mollification of the saturation velocity) for the nonlinear case and also of the exact problem for the linear case with a small coefficient in the temperature equation. Bibl. 8 titles.