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  4. Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data

Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data

MMC.
2022;
Volume 9, Number 4
: pp. 977–998
https://doi.org/10.23939/mmc2022.04.977
Received: February 14, 2022
Accepted: June 23, 2022

Mathematical Modeling and Computing, Vol. 9, No. 4, pp. 977–998 (2022)

Authors:
  1. M. B. Benboubker
  2. U. Traore
1
Higher School of Technology Sidi, Mohamed Ben Abdellah University, Fez, Morocco
2
Laboratoire de Mathématiques et Informatique (LAMI), Département de Mathématiques, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

In this paper we prove the existence of an entropy solution to nonlinear parabolic equations with diffuse Radon measure data which does not charge the sets of zero $p(\cdot)$-capacity and nonhomogeneous Neumann boundary condition.  By a time discretization technique we analyze existence, the uniqueness and the stability questions.  The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

nonlinear parabolic problem
variable exponents
entropy solution
Neumann–type boundary conditions
semi-discretization
Radon measure
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