Abstract:
In our presentation, we spotlight the theory of C0 semigroups as a fundamental tool for analyzing
evolution equations in Banach spaces. We begin by reviewing the general properties of C0
semigroups and their role in describing the time evolution of systems governed by linear operators.
The discussion then moves to the abstract Cauchy problem, emphasizing conditions for the
existence, uniqueness, and regularity of solutions using semigroup methods.
We extend these ideas to nonlinear evolution equations, highlighting techniques that address the
challenges posed by nonlinearity.
Special attention is given to delay differential equations (DFEs), where the system’s future state
depends on its history.
After providing an overview of delayed systems, we discuss two major cases: abstract linear delayed
equations and semi-linear delayed equations, showing how semigroup theory adapts to account for
memory effectsL’objectif de cet exposé est de prouver l’existence et l’unicité d’une solution d’un problème de
Goursat non linéaire dans la classe des fonctions quasi-analytiques de type Denjoy- Carleman, plus
précisément dans l’ensemble des fonctions continues Denjoy-Carleman.
L’idée est de transformer le problème integro-diferentiel à un problème de point fixe appliqué dans
une boule fermée dans une algèbre de Banach définie par une série formelle et une suite numérique
logarithméquement convexe convenablement choisieA problem of initial value problem for a nonlinear Caputo fractional differential equation on an
unbounded interval is considered. Based on some fractional calculus and the Krasnoselskii’s fixed
point theorem, we prove our main results (existence and asymptotic stability).
Then we give an example to illustrate our study.s..It is our pleasure to cordially invite all professors and
students to participate in an Open Study Day dedicated to
Ordinary Differential Equations (ODE)
& Partial Differential Equations (PDE).