Existence results for a non-linear obstacle parabolic semicoercive problems with lower order term

ABSTRACT

In this paper, we shall be concerned with the existence result of a non-linear parabolic equations associated to the form, , where the right-hand side and the initial data belong to and the lower order term is a non-coercive Carathéodory function. The growth and coercivity conditions on the monotone vector field a are prescribed by an N-function M, which does not have to satisfy the condition. Therefore, we work with an Orlicz–Sobolev spaces which are not necessarily reflexive.

KEYWORDS:

• Non-linear parabolic problems
• Orlicz–Sobolev spaces
• unilateral problems
• measurable obstacle
• lower order term

AMS SUBJECT CLASSIFICATION:

• 35K86

Acknowledgements

The authors are really grateful for all the important suggestions and remarks mentioned by the Editor and the reviewers, we thank them strongly and we would like also to express our thanks for the careful reading and helpful comments which help us to improve the presentation of the paper.

Notes

No potential conflict of interest was reported by the authors.