Plenary Speakers
CONFERENCE TITLE : Recent progress on homogenization of the bidomain and tridomain models in electrocardiology.
ABSTRACT : At the microscopic level, cardiac tissue is very complex and it is therefore very difficult to understand and predict its behavior at the macroscopic (observable) scale. To each cardiac system, we associate a microscopic model (of elliptic type), coupled to a nonlinear ODE system and another microscopic one (dynamical boundary condition). Based on Ohm's law of electrical conduction and conservation of electrical charge, we obtain the microscopic model that gives a detailed description of the electrical activity in the cells responsible for cardiac contraction. Then, using homogenization techniques (based on unfolding operators), we obtain the macroscopic model which, in turn, allows us to describe the propagation of electrical waves in the entire heart.
CONFERENCE TITLE : A bridge between discrete fixed point theory and metric fixed point theory : Metric approach to resolve some combinatorial problems
ABSTRACT : The notable comparative study between the metric fixed point theory and the discrete one finds its roots in the works of Pouzet and his collaborators. In 1986, Jawhari et al. considered a generalized metric space , where, instead of real numbers, the distance values are members of an ordered monoid equipped with an involution satisfying a distributivity condition. They showed that Tarski’s classical fixed point theorem is closely related to Sine-Soardi theorem. Indeed, complete lattices may be seen as hyperconvex metric spaces.
In 2020, Khamsi and Pouzet established an analogy between metric spaces and binary relational systems. By extending Penot’s notions, they gave an abstract version of Kirk’s result in this framework. In 2022, El adraoui et al. considered a generalized metric space (E, d), where the metric takes their values in a binary relational system verifying some special conditions. Using a generalization of the constructive lemma due to Gillespie and Williams,they proved that if the space (E, d) has compact and normal structure, then every nonexpansive mapping has a fixed point. They obtained Tarski’s fixed point theorem as a corollary.
This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relational systems and the existence of fixed point for nonexpansive mappings in metric spaces.
CONFERENCE TITLE : Periodic Solutions and Attractivness for some Partial Functional Differntial Equations with Lack of Compactness.
ABSTRACT : This work deals with the existence of periodic solutions and attractiveness for some partial functional differential equations in Banach spaces.
We assume that the first linear part generates a strongly continuous semi-group, while the delayed part is periodic with respect to the first argument. We prove that the existence of a bounded solution implies the existence of a periodic solution. Several results regarding uniqueness and global attractiveness of periodic solutions are also established. The analysis relies on a fixed point theorem of Chow and Hale’s type and uses some arguments of weak topology. Our theorems extend in a broad sense some new and classical related results. An application to a transport equation with delay is also presented.
CONFERENCE TITLE : RECENT GEOMETRIC PROPERTIES OF VARIABLE EXPONENT SPACES
ABSTRACT : On an intuitive level, the variable exponent space is obtained by replacing the energy (also known as modular)
$$\int_{\Omega}^{}{|f(t)|^p}\,dt \text{ with } \int_{\Omega}^{}{|f(t)|^p(t)} \,dt$$
where p(x) is a function defined on Ω. Lately variable exponent spaces have attracted quite a bit of attention. Variable exponent spaces are connected to variational integrals with nonstandard growth and coercivity conditions. These nonstandard variational problems are related to modeling of the so called electrorheological fluids and also appear in some models related to image restoration.
In this talk, we start by a simple introduction to variable exponent spaces. Then we move to discuss some recent results related to the modular geometry of such spaces.
CONFERENCE TITLE : Some fixed point theorems in Banach spaces and application to a transport equation with delayed neutrons
ABSTRACT :
