Zhu P. An Introduction to Matched Asymptotic Expansions

Bilbao: Basque Center for Applied Mathematics and Ikerbasque Foundation for Science, 2010. — IV, 85 p.This is the lecture notes of the course on Asymptotic Analysis that I gave at The Basque Center for Applied Mathematics (BCAM) from Nov. 9 to Nov. 13, 2009, as the second of this series of BCAM courses. Here I have added some preliminary materials. In this course, we introduce some basic ideas in the theory of asymptotic analysis. Asymptotic analysis is an important branch of applied mathematics and has a broad range of contents. Thus due to the time limitation, I concentrate mainly on the method of matched asymptotic expansions.Firstly some simple examples, ranging from algebraic equations to partial differential equations, are discussed to give the reader a picture of the method of asymptotic expansions. Then we end with an application of this method to an optimal control problem, which is concerned with vanishing viscosity method and alternating descent method for optimal control of scalar conservation laws in presence of non-interacting shocks.PrefaceIntroductionAlgebraic equations
Ordinary differential equations
Partial differential equations
An application to optimal control theoryBibliography
Index