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Mhamed Eddahbi

Professor

Faculty

كلية العلوم
Department of Mathematics, College of Sciences, King Saud University, Building 4, second floor, Office Nu. 2B65, PO. Box 2455 Riyadh, Z.C. 11451
publication
Journal Article
2024

Well-posedness of a Nonlinear Stochastic Model for a Chemical Reaction in Porous Media and Applications

In this paper, we considered a stochastic model of chemical reactive flows acting through porous media under the influence of nonlinear external random fluctuations, where the interchanges of chemical flow across the skeleton's surface are represented by a nonlinear function. We studied the existence and uniqueness of strong probabilistic solutions for the model under consideration. We also show the positivity for the concentration of the solute in the fluid face as well as the concentration of reactants on the surface of the skeleton under extra reasonable assumptions on the data. Initially, we approximated the solution of the nonlinear stochastic diffusion equation using Galerkin's approximation, and obtained important bound estimates along with probabilistic compactness results. Thereafter, we passed the limit and obtained a weak probabilistic solution. This was followed by the path-wise uniqueness of the solution, which leads to the existence and uniqueness of strong probabilistic solutions as a result of Yamada-Watanabe's theorem. Finally, we discuss some important numerical applications such as Langmuir and Freundlich kinetics using the extended stochastic non-conforming finite element method to illustrate the efficiency of this approach and compare it to the deterministic approach in both cases.  Let us mention that well-posedness, positivity, and numerical simulations have not been considered so far for such a nonlinear stochastic model.

Publication Work Type
Article
Publisher Name
AIMS Mathematics
Volume Number
9
Issue Number
9
Pages
24860 to24886
more of publication
publications

In this paper, we considered a stochastic model of chemical reactive flows acting through porous media under the influence of nonlinear external random fluctuations, where the interchanges of…

by Mhamed Eddahbi, Mogtaba Mohammed, and Hammou El-Otmany
2024
Published in:
AIMS Mathematics
publications

In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic…

by E. M. B. Bouhadjar, N. Khelfallah, M.Eddahbi
2024
Published in:
Axioms
publications

The predominant approach for studying volatility is through various GARCH specifications, which are widely utilized in model-based analyses. This study focuses on assessing the predictive…

by B. Benaid, I. Al Hasani, M. Eddahbi
2024
Published in:
Symmetry