Abstract
In this paper, we study the degenerate parabolic variational inequality problem in a bounded domain. First, the weak solutions of the variational inequality are defined. Second, the existence of the solutions in the weak sense are proved by using the penalty method and the reduction method.
Highlights
We consider the initial-boundary problem of the following parabolic variational inequality:
The authors in [ ] extended the corresponding conclusions to the Rd-values case in which the existence and uniqueness of solution to parabolic variational inequalities with integrodifferential terms were proved by using the penalty method and the reduction method
In Section, we prove that for p ≥, γ ∈ (, ), problem ( ) admits a weak solution in the sense of Definition
Summary
We consider the initial-boundary problem of the following parabolic variational inequality:. The existence of solutions to problem ( ) was studied in a series of papers (see [ ] and [ ] and references therein). In [ ], Sun and Shi Journal of Inequalities and Applications (2015) 2015:204 the authors discussed a general case in which the linear parabolic operator with constant coefficients can be replaced by a quasi-linear one with integro-differential terms. The authors in [ ] extended the corresponding conclusions to the Rd-values case in which the existence and uniqueness of solution to parabolic variational inequalities with integrodifferential terms were proved by using the penalty method and the reduction method. To the best of our knowledge, the existence of solutions to the variational inequality problem with the degenerate parabolic operators has not been studied. We end the introduction by showing the following lemma which is used to prove our main results (see [ ])
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
