BODJRENOU Noudéhouénou Firmin

Affiliated CEAs:

CEA SMIA, University of Abomey-Calavi

CEA MITIC Gaston Berger University

Thesis director Mamadou Abdoul DIOP, Gaston Berger University, Senegal

Thesis co-supervisor : Carlos OGOUYANDJOU, Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi,

Other contributors to thesis supervision : Abdoulaye DIALLO, UFR des Sciences Appliquées et de Technologies, Université Gaston Berger, Saint-Louis, Senegal, diallo.abdoulaye8@ugb.edu.sn

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Scientific publications :

https://docs.google.com/document/d/11FWVkdK2_s1zNTqOsKTP5EgWbZbKHVJ-wGpf63Ti4dQ/edit

• [1] Mbarack FALL, Firmin BODJRENOU, Carlos OGOUYANDJOU and Mamadou Abdoul Diop, "Existence and controllability of impulsive stochastic integro-differential equations with state-dependent delay."
• [2] Papa Ali Thiama, Déthié Dioneb, Firmin Bodjrenouc and Mamadou Abdoul Diop, "A note on existence results for noninstantaneous impulsive integrodifferential systems."

Start date: 01/01/2023- Start date: 01/01/2023
Anticipated date of thesis defense: August 2025
ORCID profile: 0000-0003-2811-0466

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Project title: Optimal control of evolution problems with non-compact generators: deterministic and stochastic cases

Summary of the scientific project:
Research work will focus on the controllability and stability of systems of integrodifferential equations. The specific objectives in the case of evolution problems will be to seek to optimize these systems of equations under the conditions or constraints associated with them. Specifically, we will consider case-by-case (deterministic or stochastic ...) space sets, constraints and other related measures of controllability and stability.

Summary of results obtained:
- The aim of this study is to investigate the existence of smooth solutions for a class of impulsive stochastic integrodifferential equations with state-dependent delay in a separable real Hilbert space, as well as the controllability of these solutions. We propose sufficient conditions for the existence and controllability results using fixed-point techniques combined with Grimmer's resolvent operator theory and stochastic analysis. Finally, we give an example to illustrate the results obtained [1].
- A class of non-instantaneous impulsive integrodifferential systems in a Banach space will be the focus of the research presented in this paper. First, we formulate the existence and uniqueness of smooth solutions for the equation under consideration with local initial conditions. The problem is then solved step by step using the Grimmer resolution operator combined with the Banach contraction theorem. Furthermore, considering the scenario in which we provide our system with non-local initial conditions, Krasnoselskii's fixed point theorem is used to establish soft solutions. To illustrate the theory, we'll look at two different examples [2].