عنوان

Applied Theory of Functional Differential Equations

(Number (ISBN

9048142156

(Number (ISBN

9401580847

(Number (ISBN

9789048142156

(Number (ISBN

9789401580847

Number

b591902

Title Proper

Applied Theory of Functional Differential Equations

General Material Designation

[Book]

First Statement of Responsibility

by V. Kolmanovskii, A. Myshkis.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands : Imprint : Springer

Date of Publication, Distribution, etc.

1992

Specific Material Designation and Extent of Item

(XVI, 234 pages)

Series Title

Mathematics and Its Applications (Soviet Series),, 85.

Text of Note

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. Stocnastic 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 stochastic 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 stochastic delay systems --; 1. Dynamic programming method for controlled stochastic 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 stochastic systems with delay --; 1. Filtering of Gaussian processes --; 2. Filtering of solutions of Itô equations with delay.

Text of Note

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 stochastic 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.

Mathematics.

Mechanical engineering.

Systems theory.

by V. Kolmanovskii, A. Myshkis.

A Myshkis

V Kolmanovskii

Electronic name

[Book]

Y