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  4. Anisotropic parabolic problem with variable exponent and regular data

Anisotropic parabolic problem with variable exponent and regular data

MMC.
2022;
Volume 9, Number 3
: pp. 519–535
https://doi.org/10.23939/mmc2022.03.519
Received: November 19, 2021
Revised: February 06, 2022
Accepted: February 07, 2022

Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 519–535 (2022)

Authors:
  1. Rabah Mecheter
1
Department of Mathematics and Informatics, University of M'sila, M'sila, Algeria, Laboratory of Functional Analysis and Geometry of Spaces

In this paper, we study the existence of weak solutions for a class of nonlinear parabolic equations with regular data in the setting of variable exponent Sobolev spaces.  We prove a "version" of a weak Lebesgue space estimate that goes back to "Lions J. L. Quelques méthodes de résolution des problèmes aux limites. Dunod, Paris (1969)" for parabolic equations with anisotropic constant exponents ($p_i(\cdot)=p_i$).

anisotropic parabolic
nonlinear parabolic equations
regular data
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