Integrodifferential Equations with Non-autonomous Operators
نویسنده
چکیده
The result of Da Prato and Sinestrari [3] concerning the non-autonomous evolution operators of hyperbolic type for the equation u′(t) = A(t)u(t) + f(t), t ∈ [0, T ], w(0) = w0, is applied to the study of u′(t) = A(t) [ u(t)+ ∫ t −∞ G(t, s)u(s)ds ] +K(t)u(t)+f(t), t ∈ [0, T ], u(s) = φ(s), s ≤ 0, which models linear viscoelasticity. Here A(·) satisfies all the requirements of Kato’s semigroup approach except for the density of the common domain of A(t). An application in linear viscoelasticity is given. AMS (MOS) subject classification : 45K, 45N.
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