Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: An infinite horizon linear-quadratic optimal control problem for a singularly perturbed system with multiple point-wise and distributed small delays in the state variable is considered and the zero-order asymptotic solution is constructed.
Abstract: An infinite horizon linear-quadratic optimal control problem for a singularly perturbed system with multiple point-wise and distributed small delays in the state variable is considered. The set of Riccati-type equations, associated with this problem by the control optimality conditions, is studied. Since the system in the control problem is singularly perturbed, the equations of this set are also perturbed by a small parameter of the singular perturbations. The zero-order asymptotic solution to this set of equations is constructed and justified. Based on this asymptotic solution, parameter-free sufficient conditions for the existence and uniqueness of solution to the original optimal control problem are established.
18 citations
Journal Article•
TL;DR: In this article, the authors studied the asymptotic behavior of solutions to the Korteweg-deVries-Burgers equation in the case when the initial data has different scaling factors at different scales.
Abstract: In this work we study the asymptotic behaviour of solutions to the Korteweg--deVries--Burgers equation in the case when the initial data has different asymptotic limits at $\pm\infty $ The method used is the one developed by Kawashima and Matsumura to discuss the asymptotic behaviour of travelling-wave solutions to Burgers equation
18 citations
TL;DR: In this article, an analysis of mixed convection effects in a wall plume flow is presented, where the results apply downstream from the source and the method of matched asymptotic expansions has been used to obtain a consistent solution.
18 citations
Book•
01 Feb 1996
TL;DR: In this paper, asymptotic problems for non-linear elliptic equations in cylindrical domains and homogenization problems are studied. But the authors focus on homogenisation problems.
Abstract: Preface 1. Asymptotic problems for non-linear elliptic equations 2. On the asymptotic behaviour of solutions of some non-linear elliptic equations in cylindrical domains 3. On the asymptotic behaviour of solutions of non-linear elliptic equations in a neighbourhood of a conic point of the boundary 4. On some homogenization problems Index.
18 citations
TL;DR: A numerical method based on an iterative scheme is proposed for a singularly perturbed delay differential equation of reaction-diffusion type and the solution of the delay problem is obtained as the limit of the solutions to a sequence of the non-delay problems.
18 citations