Raafat Talhouk

@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}

}