Ovidiu Carja, Ioan I. Vrabie's Applied Analysis and Differential Equations: Iasi, Romania, PDF

By Ovidiu Carja, Ioan I. Vrabie

ISBN-10: 9812705945

ISBN-13: 9789812705945

This quantity includes refereed learn articles written by way of specialists within the box of utilized research, differential equations and similar subject matters. recognized top mathematicians world wide and trendy younger scientists conceal a various diversity of issues, together with the main fascinating fresh advancements. A large diversity of subject matters of modern curiosity are taken care of: life, distinctiveness, viability, asymptotic balance, viscosity options, controllability and numerical research for ODE, PDE and stochastic equations. The scope of the booklet is extensive, starting from natural arithmetic to varied utilized fields corresponding to classical mechanics, biomedicine, and inhabitants dynamics

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Extra info for Applied Analysis and Differential Equations: Iasi, Romania, 4-9 September 2006

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33) 0 Proof. Let {S(t); t ≥ 0} be the semigroup of contractions generated by the operator A. g. Ref. 12, Sect. 1) to deduce the existence of a unique solution U (t) to the problem (28), given by t U (t) = S(t)U 0 + S(t − s)F (s) ds, 0 Hence, we derive the inequality (33). t ∈ [0, t0 ]. January 8, 2007 20 18:38 WSPC - Proceedings Trim Size: 9in x 6in icaade M. Bˆırsan We mention that the estimate (33) expresses the continuous dependence of the solution upon the initial data {u0 , v 0 , δ 0 , w0 , ϕ0 , λ0 , ψ 0 , µ0 } and the external body loads {f i , li , p, P }.

K Then {un ; n ∈ N } is relatively compact. For details, see Ref. 5. 2. A function ω : R+ → R+ which is continuous, nondecreasing and the only solution of the Cauchy problem x (t) = ω(x(t)) x(0) = 0. is x ≡ 0 is called a uniqueness function. 2. If ω : R+ → R+ is a uniqueness function, then, for each k > 0, kω is a uniqueness function too. 3. Let ω : R+ → R+ be a uniqueness function and let (γk )k be strictly decreasing to 0. Let (xk )k be a bounded sequence of measurable functions, from [ 0, T1 ] to R+ , such that t xk (t) ≤ γk + ω(xk (s)) ds, 0 for k = 1, 2, ...

For x ∈ Ω. Let (u, v) : R+ × Ω → R+ × R+ be a mild solution of (12). e. e. for x ∈ Ω. Let K ⊆ R × L2 (Ω) × L2 (Ω) be defined by K = (t, u, v) ∈ R+ × L2 (Ω) × L2 (Ω); (u, v) satisfy (16) below . e. for x ∈ Ω. 1. , be a bounded domain with C 2 boundary Γ, let f : R × R → R+ , g : R × R → R− , f : R × R → R+ and g : R × R → R− be continuous such that (11) are satisfied. , 5 such that |f (u, v)| ≤ c1 |u| + c2 , and |g(u, v)| ≤ c3 |u| + c4 |v| + c5 for each (u, v) ∈ R × R. e. e. for x ∈ Ω. Let K be defined by (15).

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Applied Analysis and Differential Equations: Iasi, Romania, 4-9 September 2006 by Ovidiu Carja, Ioan I. Vrabie

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