Applied Theory of Functional Differential Equations / Edition 1

by V. Kolmanovskii, A. Myshkis

Overview

This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems).
The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and shastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8.
For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

Product Details

ISBN-13:	9780792320135
Publisher:	Springer Netherlands
Publication date:	11/30/1992
Series:	Mathematics and its Applications , #85
Edition description:	1992
Pages:	234
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

1. Models.- 1. Formal prerequisites.- 2. Aftereffect in mechanics.- 3. Hereditary phenomena in physics.- 4. Models with delays in technical problems.- 5. Aftereffect in biology.- 6. Aftereffect in medicine.- 7. Aftereffect in economy and other sciences.- 2. General theory.- 1. Introduction. Method of steps.- 2. Cauchy problem for RDEs.- 3. Cauchy problem for NDEs.- 4. Differential inclusions of retarded type (RDIs).- 5. General linear equations with aftereffect.- 6. Linear autonomous equations.- 7. Hopf bifurcation.- 8. Snastic retarded differential equations (SRDEs).- 3. Stability of retarded differential equations.- 1. Liapunov’s direct method.- 2. Linear autonomous equations.- 4. Stability of neutral type functional differential equations.- 1. Direct Liapunov’s method.- 2. Stability of linear autonomous equations.- 5. Stability of shastic functional differential equations.- 1. Statement of the problem.- 2. Liapunov’s direct method.- 3. Boundedness of moments of solutions.- 6. Problems of control for deterministic FDEs.- 1. The dynamic programming method for deterministic equations. Bellman’s equation.- 2. Linear quadratic problems.- 3. Optimal control of bilinear hereditary systems.- 4. Control problems with phase constraint formula.- 5. Necessary optimality conditions.- 7. Optimal control of shastic delay systems.- 1. Dynamic programming method for controlled shastic hereditary processes.- 2. The linear quadratic problem.- 3. Approximate optimal control for systems with small parameters.- 4. Another approach to the problem of optimal synthesis control.- 8. State estimates of shastic systems with delay.- 1. Filtering of Gaussian processes.- 2. Filtering of solutions of Itô equations with delay.