Introduction to the theory and applications of functional differential equations

>> Google Books

所蔵情報QRコード

Introduction to the theory and applications of functional differential equations / by V. Kolmanovskii and A. Myshkis

資料種別:

図書

出版情報:

Dordrecht ; Boston : Kluwer Academic Publishers, c1999

形態:

xvi, 648 p. ; 25 cm

シリーズ名:

Mathematics and its applications ; v. 463 <BA00044495>

著者名:

ISBN:

9780792355045 [0792355040] (: hd : alk. pap)

書誌ID:

BA40216574

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references(p. 601-641) and index

主題:

Functional differential equations

言語:

英語

目次情報:

Preface

Modelling by Functional Differential Equations / Part I.：

Theoretical preliminaries / Chapter 1.：

Functional differential equations (FDEs) / 1.：

Some classes of FDEs / 1.1：

Solution concept for a FDE / 1.2：

FDE with retardation / 1.3：

A little bit of philosophy / 1.4：

Models / Chapter 2.：

Viscoelasticity

Aftereffect in mechanics / 2.：

Motion of a particle in a liquid / 2.1：

Controlled motion of a rigid body / 2.2：

Models of polymer crystallization / 2.3：

Stretching of a polymer filament / 2.4：

Hereditary phenomena in physics / 3.：

Dynamics of oscillation / 3.1：

Relativistic dynamics / 3.2：

Nuclear reactors / 3.3：

Distributed networks (long line with tunnel diode) / 3.4：

Heat flow in materials with memory / 3.5：

Models of lasers / 3.6：

Neural network / 3.7：

Models with delays in technical problems / 4.：

Infeed grinding and cutting / 4.1：

Technological delay / 4.2：

Car chasing / 4.3：

Ship course stabilization / 4.4：

Process of combustion in small rockets / 4.5：

Delay-differential equations in engineering applications / 4.6：

Aftereffect in biology / 5.：

Evolution equations of a single species / 5.1：

Interaction of two species / 5.2：

Population dynamics model of N interacting species / 5.3：

Coexistence of competitive micro-organisms / 5.4：

Control problems in ecology / 5.5：

Control problems in microbiology (chemostat models) / 5.6：

Nicholson blowflies model / 5.7：

Helical movement of tips of growing plants / 5.8：

Grazing system / 5.9：

Aftereffect in medicine / 6.：

Mathematical models of the sugar quantity in blood / 6.1：

Model of arterial blood pressure regulation / 6.2：

Cancer chemotherapy / 6.3：

Mathematical models of learning / 6.4：

Mathematical models in immunology and epidemiology / 6.5：

Model of the human immunodeficiency virus (HIV) epidemic / 6.6：

Model of survival of red blood cells / 6.7：

Vision process in the compound eye / 6.8：

Human respiratory system / 6.9：

Regulation of glucose-insulin system / 6.10：

A disease transmission model / 6.11：

Aftereffect in economy and other sciences / 7.：

Optimal skill with retarded controls / 7.1：

Optimal advertising policies / 7.2：

Commodity price fluctuations / 7.3：

Model of the fishing process / 7.4：

River pollution control / 7.5：

Control of financial management / 7.6：

Theoretical Background of Functional Differential Equations / Part II.：

General theory / Chapter 3.：

Introduction. Method of steps

Notation

Cauchy problem for FDEs

Steps method for FDEs of retarded type (RDEs)

Steps methods for FDEs of neutral type (NDEs)

Problem for a process with aftereffect renewal / 1.5：

Cauchy problem for RDEs

Basic solvability theorem

Variants

Semigroup relation

Absolutely continuous solutions

RDEs with infinite delay / 2.5：

Features of the Cauchy problem for RDEs / 2.6：

Cauchy problem for NDEs

Smooth solutions

NDEs with a functional of integral type

Application of the steps method

Transition to the operator equation

Hale's form of NDEs

Differential inclusions of retarded type (RDIs)

Introduction

Multimaps

Solvability of the Cauchy problem for RDIs

Generalized solutions of RDEs and RDIs

General linear FDEs with aftereffect

Cauchy problem for linear RDEs

Generalization

Integral representation for the solution of the Cauchy problem (variation of constants formula)

Adjoint equation. Periodic solutions

Linear NDEs

Simplest nonautonomous RDEs of the first and second orders

Linear autonomous FDEs

Exponential solutions of linear autonomous RDEs

Solution of the Cauchy problem

Example of a showering person

Linear autonomous NDEs

Hopf bifurcation of FDEs

Example

General case

Example of an RDE with constant delay: intraspecific struggle for a common food

Example of an RDE with autoregulative delay: combustion in the chamber of a turbojet engine

Example NDE: auto-oscillation in a long line with tunnel diod / 7.7：

Stochastic retarded differential equations (SRDEs) / 8.：

Initial value problem / 8.1：

Existence and uniqueness of solution / 8.2：

Some characteristics of solutions of linear equations / 8.3：

Stability / Part III.：

Stability of retarded differential equations / Chapter 4.：

Liapunov's direct method

Stability definitions

Stability theorems for equations with bounded delay

Stability of equations with unbounded delay

Stability of linear nonautonomous RDEs

Stability of linear periodic RDEs

Application of comparison theorems / 1.6：

Stability in the first approximation / 1.7：

Case of non-positive derivative / 1.8：

Linear autonomous RDEs

Laplace transformation

Stability conditions

Stability investigation methods for linear autonomous RDEs

Mikhailov criterium

Scalar n-th order equations

Equations with discrete delays

Razumikhin's method

Guiding functions for systems without delay

Guiding functionals for RDEs

Direct application of Liapunov functions to RDEs

The main idea of B.S. Razumikhin

"Impossibility of the first breakdown"

Precize formulation / 4.7：

Connection between Razumikhin's method and Liapunov functionals / 4.8：

Asymptotic stability / 4.9：

Refinement of estimations / 4.10：

Transformation of RDEs / 4.11：

Other applications of Razumikhin's method / 4.13：

Stability of RDEs with autonomous linear part / Chapter 5.：

Notations

L[superscript 2]-stability

Estimates for the Green function

A bound for a region of attraction

Liapunov functionals for concrete FDEs / Chapter 6.：

Statement of the problem

Formal description of the procedure

Dissipative systems

Exponential contractivity

Exponentially stable linear part

Smooth coefficients

Scalar RDEs

Scalar equations of n-th order

Scalar equations of second order

Stability of chemostat

Riccati type stability conditions of some linear systems with delay / Chapter 7.：

Special case

The stability condition for this case

An application of a form of NDE

One more stability condition

Discrete delay-independent stability conditions

Delay-dependent stability conditions for equations with discrete delays

The stability condition

Distributed delay

Stability of neutral type functional differential equations / Chapter 8.：

Direct Liapunov's method

Degenerate Liapunov functionals

Stability in a first approximation

The use of functionals depending on derivatives

Instability of NDEs

Stability of linear NDEs

Scalar NDEs

Stability of NDEs with discrete delays

The influence of small delays on stability

Linear inhomogeneous NDEs

Boundedness of derivatives for linear NDEs

Boundedness of derivatives for nonlinear NDEs / 2.7：

Linear periodic NDEs / 2.8：

Application of the direct Liapunov method / Chapter 9.：

Description of the procedure

Scalar NDEs of n-th order

Another stability condition

The summarizing result

Nonlinear NDEs

Stability of the second order NDEs

An illustrative example for dimension n = 3

Matrix Riccati equations in stability of NDEs

Stability of stochastic functional differential equations / Chapter 10.：

Definitions of stability

Ito's formula

Examples

Exponential stability

Stability under persistent disturbances

Boundedness of moments of solutions

General conditions for boundedness of moments

Scalar SRDE

Second order SRDE

Construction of Liapunov functionals for SNDEs

Scalar SNDE

Nonlinear example

Riccati matrix equations in stability of linear SRDEs

Boundary Value Problems and Periodic Solutions of Differential Equations / Part IV.：

Boundary value problems for functional differential equations / Chapter 11.：

Boundary value problems for FDEs of evolutionary type

Problems with a finite defect

Halanay's boundary value problem

Periodic problem

Boundary value problems for FDEs of nonevolutionary type

FDEs with unique principal term

FDEs with nonunique principal term

Fredholm alternative for periodic solutions of linear FDEs / Chapter 12.：

Existence of periodic solutions

Conditions of the Fredholm alternative validity

Connection between boundedness and periodicity

Periodic solution of linear difference equations (DcEs)

Stationary case. Commensurable shifts of the argument

Arbitrary delays

Variable coefficients, delays divisible by a period

Variable coefficients, delays commensurable with a period

Variable coefficients, arbitrary constant delays

NDEs with small nonlinearities

Periodic solutions of autonomous FDEs with small parameter

Generalized periodic solutions of Functional Differential Equations / Chapter 13.：

Some prerequisites

Conditions of existence of periodic solutions

Relation between stability and periodicity

Stability of periodic solutions

Periodic solutions of concrete classes of equations

The case of quasilinear deterministic equation

Linear equations

Periodic solutions of the Ito's SFDEs

Scalar SRDEs

Method of Liapunov functionals

Uniqueness of periodic solutions

Control and Estimation in Hereditary Systems / Part V.：

Problems of control for deterministic FDEs / Chapter 14.：

The dynamic programming method for deterministic RDEs. Bellman's equation

Optimality conditions

Linear quadratic problems

Optimal control synthesis

Exact solution

Systems with delays in the control

Effects of delays in regulators

NDE

Optimal control of bilinear hereditary systems

Construction of the optimal control synthesis

Model of optimal feedback control for microbial growth

Control problems with phase constraint formula

General optimality conditions

Necessary optimality conditions

Systems with state delays

Systems with distributed delays

Linear systems with discrete and distributed delays

Neutral type systems

Adaptive control of FDEs

Scalar equations

Delay identification

Multidimensional systems

Optimal control of stochastic delay systems / Chapter 15.：

Dynamic programming method for controlled stochastic hereditary processes

The linear quadratic problem

Bellman functional and optimal control

Approximate solution

Some generalizations

Approximate optimal control for equations with small parameters

Formal algorithm

Quasilinear systems with quadratic cost

Another approach to the problem of optimal synthesis control

Admissible functionals

Quasilinear quadratic problems

State estimates of stochastic systems with delay / Chapter 16.：

Filtering of Gaussian processes

Problem statement

Integral representation for the optimal estimate

The fundamental filtering equation

Dual optimal control problem

Particular cases

Dependence of the error of the optimal estimate on the delay

Filtering of solutions of Ito's equations with delay

Dual control problem

Minimax filtering in systems with delay

Bibliography

Index

Preface

Modelling by Functional Differential Equations / Part I.：

Theoretical preliminaries / Chapter 1.：

Functional differential equations (FDEs) / 1.：

Some classes of FDEs / 1.1：

Solution concept for a FDE / 1.2：

続きを見る

東工大ブックレビュー

類似資料:

1 図書 Applied theory of functional differential equations Kolmanovskiĭ, Vladimir Borisovich, Myshkis, A. D. (Anatoliĭ Dmitrievich) Kluwer Academic Publishers	7 図書 Functional differential operators and equations (: alk. paper) Kurbatov, V. G. (Vitaliĭ Gennadʹevich) Kluwer Academic Pub.
2 図書 Theory and applications of partial functional differential equations Wu, Jianhong Springer	8 図書 Functional differential equations (: us ; : gw) Hale, Jack K., 1928- Springer-Verlag
3 図書 Stability of functional differential equations (: hbk ; : pbk) Kolmanovskiĭ, Vladimir Borisovich, Nosov, V. R. Academic Press	9 図書 Lineare Differentialgleichungen mit nacheilendem Argument Myshkis, A. D. (Anatoliĭ Dmitrievich) VEB Deutscher Verlag der Wissenschaften
4 図書 Theory of functional differential equations (: us ; : gw ; : softcover) Hale, Jack K., 1928- Springer-Verlag	10 図書 Лекции по высшей математике Myshkis, A. D. (Anatoliĭ Dmitrievich) Изд-во "Наука", Главная редакция физико-математической литературы
5 図書 Elliptic functional differential equations and applications (: us ; : sz) Skubachevskiĭ, A. L Birkhäuser Verlag	11 図書 Functional differential equations : proceedings of the International Symposium : Kyoto, Japan, 30 August-2 September 1990 International Symposium on Functional Differential Equations and Related Topics, 吉沢, 太郎, 加藤, 順二 World Scientific, c1991
6 図書 Functional differential equations : application of i-smooth calculus Kim, A. V. Kluwer Academic	12 図書 Low-gravity fluid mechanics : mathematical theory of capillary phenomena (: us ; : gw) Myshkis, A. D. (Anatoliĭ Dmitrievich), Wadhwa, R. S. Springer-Verlag