Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces
نویسندگان
چکیده
and Applied Analysis 3 For every h ∈ L1([0, a],X), the right-hand side of (21) is a continuous function on [0, a]. It is natural to consider it as a generalized solution of (8) even it is not differentiable and dose not strictly satisfy the equation. We therefore define the following. Definition 2. Let −A is the infinitesimal generator of C 0 semigroup T(t) (t ≥ 0). Then a continuous solution u(t) of the integral equation u (t) = S 2 (t) x 0 + ∫ t 0 S 2 (t − s) S 1 (s) v 0 ds
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