Existence and uniqueness of renormalized periodic solution to a nonlinear parabolic problem with variable exponent and L1 data

We consider a class of nonlinear periodic equations having p(x)-growth conditions and L1 data. By using generalized Lebesgue and Sobolev spaces with variable exponent, we establish the existence and uniqueness of a renormalized periodic solution to the studied problem.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-02, Vol.506 (2), p.125674, Article 125674
Main Authors: Charkaoui, Abderrahim, Alaa, Nour Eddine
Format: Article
Language:English
Subjects:
[formula omitted] data
Periodic solutions
Renormalized solutions
Variable exponent
Weak solutions
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Summary:We consider a class of nonlinear periodic equations having p(x)-growth conditions and L1 data. By using generalized Lebesgue and Sobolev spaces with variable exponent, we establish the existence and uniqueness of a renormalized periodic solution to the studied problem.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125674