Stability of solutions to abstract evolution equations with delay
نویسنده
چکیده
An equation u̇ = A(t)u+B(t)F (t, u(t−τ)), u(t) = v(t),−τ ≤ t ≤ 0 is considered, A(t) and B(t) are linear operators in a Hilbert space H, u̇ = du dt , F : H → H is a non-linear operator, τ > 0 is a constant. Under some assumption on A(t), B(t) and F (t, u) sufficient conditions are given for the solution u(t) to exist globally, i.e, for all t ≥ 0, to be globally bounded, and to tend to zero at a specified rate as t→∞. MSC: 34G20, 34K20, 37L05, 47J35
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تاریخ انتشار 2011