Intervenants

Yahyaoui AMira

Identification of a Robin Coefficient from Partial Boundary Measurements.

This work addresses the identification of a Robin coefficient on an inaccessible part of the boundary of an elliptic domain from partial Cauchy data. The problem is formulated as a Tikhonov-regularized optimal control problem. We provide a variational analysis of the direct and inverse problems, derive the linearized and adjoint equations, and obtain a gradient-based reconstruction method. We also establish a convergence rate result under suitable source conditions. Numerical experiments based on a Wendland kernel discretization and an Adam-type optimization algorithm are presented to illustrate the effectiveness of the reconstruction method.

JABRANE ANIS

A BIOECONOMIC MODEL OF AN AGE-STRUCTURED FISHERY WITH ADAPTIVE EFFORT AND PRICE DYNAMICS

This paper presents and analyzes a bioeconomic model describing the interaction between an age-structured fish population, the fishing effort, and the market price dynamics. The model combines an age-structured partial differential equation for the fish population with two ordinary differential equations governing the evolution of fishing effort and price. The equilibria of the system, corresponding to the extinction, no-fishing, and sustainable fishing states, are characterized, and their local stability properties are investigated.

Numerical simulations are performed to illustrate the theoretical results and to highlight the influence of key biological and economic parameters on the persistence or collapse of the fishery. The results show that the net reproductive rate plays a decisive role as a threshold parameter: when it exceeds unity, the fishery admits a positive and stable equilibrium, representing a sustainable exploitation regime; otherwise, the population tends to extinction, leading to the disappearance of fishing activity.

SAMAALI ANIS

Résolution des problèmes de complétion de données en élasticité linéaire par des approches de contrôle optimal basées sur la méthode de Nitsche

In the present work, we focus on the resolution of the Cauchy elasticity problem using an energetic variational minimization approach in the framework of a finite element method. A new strategy of regularization, called a filtering procedure regularization, is developed. The advantage of using this new regularization is that it does not require a regularization parameter and is easy to implement. An optimal a priori error estimate is proven, for the first time up to our knowledge, in the context of the finite element method. Some numerical results are presented to illustrate the performance of our approach.

Hafyene Nabil

A data Completion Problem by Reproducing Kernels in Hilbert Spaces

In this study, we address the classical ill-posed Cauchy problem for the Laplace equa-

tion. We reformulate this inverse problem as an ill-posed interfacial equation using c-

titious domain decomposition tools. To ensure a stable reconstruction, we propose a dis-

cretized Tikhonov regularization within reproducing kernel Hilbert spaces constructed with

radial basis functions, where the associated native space coincides with Sobolev spaces.

Furthermore, we establish convergence results and error estimates. Finally, numerical

simulations are presented to highlight the performance of the proposed approach.

Guesmi anouer

Modèle de déconvolution : rééchantillonnage naïf en action

Dans cet exposé, nous nous intéressons au problème de la modélisation non paramétrique par méthodes à noyaux dans un cadre de déconvolution partielle, lorsque la covariable observée est entachée d'une erreur de mesure de type ordinaire. Ce type de modèle apparaît fréquemment en statistique avec des données bruitées, notamment lorsque les variables explicatives ne sont pas directement observables.Dans ce cadre, nous développons une étude asymptotique de l'estimateur à noyau du modèle considéré. L’objectif est d’analyser ses propriétés de convergence ainsi que son comportement en présence d’erreurs de mesure. Une attention particulière est accordée au choix du paramètre de lissage (ou fenêtre), qui joue un rôle central dans la performance de l’estimation. Ce choix est traité par une stratégie de rééchantillonnage naïve, qui permet une approximation empirique du compromis biais–variance et une sélection adaptative de la fenêtre optimale.

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