Abstract
We investigate the well-posedness (existence and uniqueness) of solutions to nonlinear parabolic problems with variable exponents and irregular data. Firstly, we establish the existence and uniqueness of weak solutions to the studied model when the data are regular enough. Secondly, we assume that the data belongs only to L1 and we prove the existence and uniqueness of both renormalized and entropy solutions. Finally, we demonstrate the equivalence between the renormalized and entropy notion of solutions to the considered problems. Our approach is based essentially on the use of truncation methods and involves some new technical estimates.
Sign-in/Register to access full text options 
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.
