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

Article type: Research Article

Authors: Perjan, Andrei | Rusu, Galina

Affiliations: Department of Mathematics and Informatics, Moldova State University, A. Mateevici str. 60, MD 2009, Chisinau, Moldova. Tel./Fax: +373 2257 7627; E-mails: [email protected], [email protected]

Abstract: We study the behavior of solutions to the problem ε(u″ε(t)+A1uε(t))+u′ε(t)+A0uε(t)+B(uε(t))=fε(t), t∈(0,T], uε(0)=u0ε, u′ε(0)=u1ε, in the Hilbert space H as ε→0, where A1, A0 are two linear self-adjoint operators and B is a Lipschitzian operator.

Keywords: singular perturbation, abstract second-order Cauchy problem, boundary layer function, a priori estimate

DOI: 10.3233/ASY-2011-1043

Journal: Asymptotic Analysis, vol. 74, no. 3-4, pp. 135-165, 2011