Raafat Talhouk

@article{safa_3033,

title = {Asymptotic Expansion of the Solutions to a Regularized Boussinesq System (Theory and Numerics)},

author = {Ahmad Safa and Hervé Le Meur and Jean-Paul Chehab and Raafat Talhouk},

url = {https://link.springer.com/article/10.1007/s10440-024-00660-3?utm_source=rct_congratemailt&utm_medium=email&utm_campaign=nonoa_20240603&utm_content=10.1007/s10440-024-00660-3},

year  = {2024},

date = {2024-06-01},

journal = {Acta Applicandae Mathematicae},

volume = {191},

number = {12},

pages = {1-25},

abstract = {We consider the propagation of surface water waves described by the Boussinesq system. Following (Molinet et al. in Nonlinearity 34:744-775, 2021), we introduce a regularized Boussinesq system obtained by adding a non-local pseudo-differential operator define by  with . In this paper, we display a twofold approach: first, we study theoretically the existence of an asymptotic expansion for the solution to the Cauchy problem associated to this regularized Boussinesq system with respect to the regularizing parameter . Then, we compute numerically the function coefficients of the expansion (in ) and verify numerically the validity of this expansion up to order 2. We also check the numerical  stability of the numerical algorithm.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{berjawi_3055,

title = {Well-posedness of the Green-Naghdi model for an uneven bottom in presence of the Coriolis effect and surface tension},

author = {Marwa Berjawi and Toufic El Arwadi and Samer Israwi and Raafat Talhouk},

url = {https://doi.org/10.1111/sapm.12725},

year  = {2024},

date = {2024-06-01},

journal = {Studies in Applied Mathematics},

abstract = {The objective of this work is to derive and analyze a

Green-Naghdi model with Coriolis effect and surface

tension in nonflat bottom geometry. Gui et al. derive

a Green-Naghdi-type model in flat bottom geometry

under the gravity and Coriolis effect. Chen et al. proved

the existence and uniqueness of solution in Sobolev

space under a condition depending on the initial velocity

and the Coriolis effect. In this paper, we provide a rigorous

derivation of Green-Naghdi model under the influence

of the two mentioned effects, with nonflat bottom.

After that, the existence and construction of solutions for

the derived model will be proved under two alternative

conditions: the first one is the same condition as in Chen

et al. and Berjawi et al. and the second one concerns only

the Coriolis coefficient ? that supposed to be only of

order ?(

?

?). This existence and uniqueness result ameliorate

the result of Chen et al. and Berjawi et al. in the

sense that no condition on the velocity is needed.We also

prove the continuity of the associated flow map.},

keywords = {},

pubstate = {online},

tppubtype = {article}

}

@article{mheich_2862,

title = {On the Logarithmic Cahn-Hilliard Equation with General Proliferation Term},

author = {RIM MHEICH and Madalina Petcu and Raafat Talhouk},

url = {https://www.aimsciences.org/article/doi/10.3934/cpaa.2024016



doi:10.3934/cpaa.2024016},

year  = {2024},

date = {2024-03-01},

journal = {Communications On Pure And Applied Analysis},

volume = {23},

number = {3},

pages = {383-403},

abstract = {Our aim in this article is to study the well-posedness of the generalized

logarithmic nonlinear Cahn-Hilliard equation with regularization and

proliferation terms. We are interested in studying the asymptotic behavior, in

terms of finite-dimensional attractors, of the dynamical system associated with

the problem and majorate the rate of convergence between the solutions of the

Cahn-Hilliard equation and the regularized one. Additionally, we present some

further regularity results and subsequently prove a strict separation property

of the solution. Finally, we provide some numerical simulations to compare the

solution with and without the regularization term, and more.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{talhouk_2369,

title = {On well-posedness for some Korteweg-de Vries type equations with variable coefficients},

author = {Raafat Talhouk and Luc Molinet and Ibtissame Zaiter},

url = {https://doi.org/10.1007/s00028-023-00904-z},

year  = {2023},

date = {2023-07-01},

journal = {Journal Of Evolution Equations},

volume = {23},

number = {3},

pages = {52},

abstract = {In this paper, KdV-type equations with time- and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of uxxx is positive and uniformly bounded away from zero and that a primitive function of the ratio between the anti-dissipation and the dispersion coefficients is bounded from below, we prove the existence and uniqueness of a solution u such that hu belongs to a classical Sobolev space, where h is a function related to this ratio. The LWP in Hs(R), s > 1/2, in the classical (Hadamard) sense is also proven under this time an assumption of boundedness of the above primitive function. Our approach combines a change of unknown with dispersive estimates. Note that previous results were restricted to Hs(R), s > 3/2, and only used the dispersion to compensate the anti-dissipation and not to lower the Sobolev index required for well-posedness.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{bader_1995,

title = {Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 - Derivation of the macroscopic tridomain model by unfolding homogenization method},

author = {Fakhrielddine Bader and Mostafa Bendahmane and Mazen Saad and Raafat Talhouk},

url = {https://doi.org/10.3233/ASY-221804},

year  = {2023},

date = {2023-05-01},

journal = {Asymptotic Analysis},

volume = {132},

number = {3-4},

pages = {575-606},

abstract = {We study the homogenization of a novel microscopic tridomain system, allowing

for a more detailed analysis of the properties of cardiac conduction than the classical bidomain

and monodomain models. In [5], we detail this model in which gap junctions are considered

as the connections between adjacent cells in cardiac muscle and could serve as alternative

or supporting pathways for cell-to-cell electrical signal propagation. Departing from this mi-

croscopic cellular model, we apply the periodic unfolding method to derive the macroscopic

tridomain model. Several diculties prevent the application of unfolding homogenization

results, including the degenerate temporal structure of the tridomain equations and a nonlin-

ear dynamic boundary condition on the cellular membrane. To prove the convergence of the

nonlinear terms, especially those dened on the microscopic interface, we use the boundary

unfolding operator and a Kolmogorov-Riesz compactness's result.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{miranville_2788,

title = {On The Cahn-Hilliard/Allen- Cahn Equations With Singular Potentials.},

author = {Alain Miranville and Wafa Saoud and Raafat Talhouk},

url = {https://doi.org/10.3934/dcdsb.2018308},

year  = {2019},

date = {2019-08-01},

journal = {Discrete And Continuous Dynamical Systems-Series B},

volume = {24},

number = {8},

pages = {3633-3651},

abstract = {The purpose of this work is to prove the existence and uniqueness of the solution for a Cahn-Hilliard/Allen-Cahn system with singular potentials (and, in particular, the thermodynamically relevant logarithmic potentials). We also prove the existence of the global attractor. Finally, we show further regularity results and we prove a strict separation property (from the pure states) in one space dimension.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{chamoun_2787,

title = {Numerical analysis of a chemotaxisswimming bacteria model on a general triangular mesh.},

author = {Georges Chamoun and Mazen Saad and Raafat Talhouk},

url = {https://doi.org/10.1016/j.apnum.2018.01.017},

year  = {2018},

date = {2018-05-01},

journal = {Applied Numerical Mathematics},

volume = {127},

number = {3},

pages = {324-348},

abstract = {This paper is devoted to the numerical study of a model arising from biology, consisting of chemotaxis equations coupled to Navier-Stokes flow through transport and external forcing. A detailed convergence analysis of this chemotaxis-fluid model by means of a suitable combination of the finite volume method and the nonconforming finite element method is investigated. In the case of nonpositive transmissibilities, a correction of the diffusive fluxes is necessary to maintain the monotonicity of the numerical scheme. Finally, many numerical tests are given to illustrate the behavior of the anisotropic Keller-Segel-Stokes system.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}