Electron. J. Diff. Equ., Vol. 2014 (2014), No. 229, pp. 1-10.

Existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time

Nabila Bellal

Abstract:
Using the penalty method, we prove the existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time. To find a solution, the original inequality is transformed into an equality by adding a positive function on the right-hand side and a complementary condition. This result can be seen as a generalization of the results by Mokrane in [11] where the obstacle is zero.

Submitted March 23, 2014. Published October 27, 2014.
Math Subject Classifications: 35K86, 35R35, 49J40.
Key Words: Parabolic variational inequalities; Leray-Lions operator; penalization; existence theorem.

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Nabila Bellal
Université 20 aoüt 1955, Skikda, Algeria.
Université Badji Mokhtar, Annaba, Algeria
email: nabilabellal@yahoo.fr

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