Convergence estimates for abstract second-order singularly perturbed Cauchy problems with Lipschitzian nonlinearities

摘要

We study the behavior of solutions to the problem {∫ ε(u_ε''(t) + A)Uε(t)) + U_ε'(t) + A_0U_ε(t) + B(u_ε(t)) = f_ε(t), t∈(0,T], u_ε(0) = U_(Qε),U'_ε(0) = u_(1ε), in the Hilbert space H as ε→ 0, where A1, A0 are two linear self-adjoint operators and B is a Lipschitzian operator.