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  4. Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces

Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces

MMC.
2021;
Volume 8, Number 4
: pp. 584–600
https://doi.org/10.23939/mmc2021.04.584
Received: May 23, 2021
Accepted: June 07, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 584–600 (2021)

Authors:
  1. A. Aberqi
  2. M. Elmassoudi
  3. M. Hammoumi
1
Sidi Mohammed Ben Abdellah University, National School of Applied Sciences, Laboratory LAMA
2
Sidi Mohammed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Laboratory LAMA, Department of Mathematics
3
Sidi Mohammed Ben Abdellah University, Poly-disciplinary Faculty of Taza, Laboratory LSI

In this paper, a  class of nonlinear evolution equations with damping arising in fluid dynamics and rheology is studied.  The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth.  The appropriate functional framework for such equations is the modularly Museilak–spaces.  The existence and uniqueness of a weak solution are proved using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given.

discrete solution
parabolic equation
weak solution
Museilak-spaces
non-standard growth
backward Euler scheme
intern approximations
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