Convergence in the boundary layer for singularly perturbed equations

✍ Scribed by Bruce A. Francis

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 459 KB
• Volume: 18
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(82)90026-7

✦ Synopsis

Under reasonable conditions the solution of a singularly perturbed initial-value problem converges as a distribution to the solution of the reduced problem. Key Wo~Linear differential equations; Laplace transforms; boundary-value problems; optimal control; singular control Abatraet--A singularly perturbed linear fmite-dimensioual ordinary differential equation is considered on the half-line [0, ®). The reduced system is assumed to have a unique solution in the sense of distributions. It is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense, and the order of the limiting distribution is computed. An application to the optimal linear-quadratic regulator with cheap control is described.