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Processus Weyl presque périodique et équations différentielles stochastiques

Abstract : The thesis deals essentialy with a class of abstract dfferential equations with Weyl almost periodic coefficients, and comprises two part. The first part is devoted to the deterministic problems, in a first step, we study the existence and uniqueness of bounded Weyl almost periodic solution to the linear abstract differential equation u’ (t) = Au(t) + f(t); t ∈ R; in a Banach space X, where A : D(A) ⊂ X → X is a linear (unbounded) operator which generates an exponentially stable C0-semigroup on X and f : R → X is a Weyl almost periodic function. Finally, in a second step, always in the same frame, we consider the semi-linear differential equation u’ (t) = Au(t) + f(t; u(t)); t ∈ R ; where f(t; u) is a Weyl almost periodic in t ∈ R; uniformly with respect compact subsets of X. The second part, is concerned with the stochastic case. Precisely, we examine the existence and uniqueness of Weyl almost periodic solution in law to the abstract semilinear stochastic evolution equation on a Hilbert separable space.
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Youcef Ibaouene. Processus Weyl presque périodique et équations différentielles stochastiques. Analyse numérique [math.NA]. Normandie Université; Université Mouloud Mammeri (Tizi-Ouzou, Algérie), 2019. Français. ⟨NNT : 2019NORMR120⟩. ⟨tel-02885035⟩

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