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.
AMS SUBJECT CLASSIFICATION:
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.