Well-posedness results to parabolic problems involving (p(x),q(x))-growth structure with L1-data

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 t...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2025-03, Vol.543 (2), p.128934, Article 128934
Main Authors: Alaa, Nour Eddine, Bendahmane, Mostafa, Charkaoui, Abderrahim
Format: Article
Language:English
Subjects:
Entropy solutions
Existence and uniqueness
Parabolic problems
Renormalized solutions
Variable exponents
Weak solutions
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Summary: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.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128934