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On the analysis of an endothermal/exothermal saturation problem. (English) Zbl 0933.35117

J. Math. Sci., New York 93, No. 5, 711-718 (1999) and Zap. Nauchn. Semin. POMI 233, 131-141 (1996).
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.
Reviewer: M.A.Vivaldi (Roma)

MSC:

35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
35K55 Nonlinear parabolic equations

Citations:

Zbl 0921.00015
Full Text: DOI EuDML

References:

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