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

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.

Keywords

• Parabolic variational inequalities
• Leray-Lions operator
• penalization
• existence theorem