On the analysis of an endothermal/exothermal saturation problem (Q1304144)

The endothermal or the exothermal saturation problem is an interesting example of a nonlinear coupled problem leading to a parabolic quasi-variational inequality. The authors investigate the solvability, in special cases, of a problem proposed by J. L. Lions (1972) which is open in the general case. Applying regularity results and inequalities of Lewy-Stampacchia type they prove the solvability of a modified, problem for the nonlinear case, and also of the exact problem for the linear case with a small coefficient in the temperature equation.