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力学和物理学中的无限维动力系统第2版(英文版)

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力学和物理学中的无限维动力系统第2版(英文版)水利图书5TS9lw+v*^^9o

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e1H4P6O&cnm\0作  者: R.Temam 著水利图书~2d0X7Jo J

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出 版 社: 世界图书出版公司

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出版时间: 2000-6-1水利图书-qrT1rVM!ow

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字  数:

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版  次: 1

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页  数: 648水利图书"fd-fDT!id {

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开  本:

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印  次:水利图书 QV:}p#P*rV`c?

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I S B N : 9787506247160

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包  装: 平装水利图书W7xoP2G}x

2yD"xA rP)t?!Rjj0所属分类: 图书 >> 自然科学 >> 力学水利图书-F;oiW#w"[fr

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内容简介水利图书%Zt }S1nv;mnK

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Since publication of the first edition of this book in 1988, the study of dynamical systems of infinite dimension has been a very active area in pure and applied mathematics; new results include the study of the existence of attractors for a large number of systems in mathematical physics and mechanics; lower and upper estimates on the dimension of the attractors; approximation of attractors; inertial manifolds and their approximation. The study of multilevel numerical methods stemming from dynamical systems theory has also developed as a subject on its own. Finally, intermediate concepts between attractors and inertial manifolds have also been introduced, in particular the concept of inertial sets.水利图书r5jJ:S}~^u

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目录水利图书Tvo2s(fY

9eI&IB [0Preface to the Second Edition水利图书5n2f$X/XX1W }I'ta

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Preface to the First Edition

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GENERAL INTRODUCTION.水利图书 ^Yc2ri%P^ s

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The User‘s Guide

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F(}!y-dmQ~0Introduction水利图书)CuTr? g@

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1. Mechanism and Description of Chaos. The Finite-Dimensional Case水利图书Ba6s`9uBz

6p4Z+G@5k?Yi02. Mechanism and Description of Chaos. The Infinite-Dimensional Case水利图书!@%idiX(a5{\Y(i A

&^M9G [t;WF\+k4F03. The Global Attractor. Reduction to Finite Dimension

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4. Remarks on the Computational Aspect

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(ab c.fd05. The User‘s Guide

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w F)N2} GN KzI0CHAPTER ⅠGeneral Results and Concepts on Invariant Sets and Attractors

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Introduction水利图书"r4z@n.x\

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1. Semigroups, Invariant Sets, and Attractors

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)q(JESx02. Examples in Ordinary Differential Equations

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3. Fractal Interpolation and Attractors水利图书y_$ZJ O })@

0R[D)z;P5X k0CHAPTERⅡ Elements of Functional Analysis水利图书(b^.h YJr

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Introduction水利图书w7^OtE ]7y%}

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1. Function Spaces水利图书 H1D:mA+k({-F\$\

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2. Linear Operators水利图书7O/h xD2G4_

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3. Linear Evolution Equations of the First Order in Time

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*y,w UH0nT04. Linear Evolution Equations of the Second Order in Time

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@&|;phId]%M f gq0CHAPTER Ⅲ Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction-Diffusion Equations. Fluid Mechanics and Pattern Formation Equations Introduction水利图书:I(S/L}'x3c U ~3k

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1. Reaction-Diffusion Equations水利图书9A:Zdd W N A @+z

%Q0[ahm7gq02. Navier-Stokes Equations(n=2)

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udH5c%W/z9O.b03. Other Equations in Fluid Mechanics

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4. Some Pattern Formation Equations

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Od!?/s gy`"b4U H05. Semilinear Equations

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,Q"e!n l1V4P06. Backward Uniqueness水利图书a9Z"}U4@ r

6\?2V_B i0CHAPTER Ⅳ Attractors of Dissipative Wave Equations水利图书 EN1} F-K

.v)zwPt;oY,_{\g$T%\0Introduction

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3zl(eMEe!K01. Linear Equations: Summary and Additional Results水利图书5t!N5AwT+d$r[#g*fx0L

:HG"vr}4}]eD@02. The Sine-Gordon Equation水利图书;hj5hw0uNy1u5L&g

'f,y%Yaf03. A Nonlinear Wave Equation of Relativistic Quantum Mechanics水利图书 y;h5^FV$lN#K^vo

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4. An Abstract Wave Equation

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Ofl.u,j\(Y05. The Ginzburg-Landau Equation水利图书H ].a(ZwU

Ghkd!y[06. Weakly Dissipative Equations. I. The Nonlinear Schr6dinger Equation水利图书+cOmV?eG~'qA

#}*oF+SS8UB@07. Weakly Dissipative Equations II. The Korteweg-De Vries Equation水利图书4z9W&\Q$F.V#?1C2r(p

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8. Unbounded Case: The Lack of Compactness水利图书,HB6TxN |&x

Fm,C m&B ^})?n\D09. Regularity of Attractors

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T:l CZ+l4]010. Stability of Attractors

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N*zQ+aq5}@"Nw0CHAPTER Ⅴ Lyapunov Exponents and Dimension of Attractors水利图书$]njy6{ h:At0y

g/X ^9U+Y0G6U0Introduction水利图书-~FK IL9t ?K

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1. Linear and Multilinear Algebra水利图书7Q Z3f3J~#C

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2. Lyapunov Exponents and Lyapunov Numbers

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3. Hausdorff and Fractal Dimensions of Attractors水利图书"Yn})m2KO!I B

I&L1s{ ~!B"Y0CHAPTER Ⅵ Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems

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8Uu4zlON/K\0Introduction水利图书I#Zl5`BBU%v C

2j"t c V f a}R!?Et$s01. The Lorenz Attractor水利图书R0q,Ot0vg,t

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2. Reaction-Diffusion Equations水利图书qQ-C2g'^

Vrr9iG8gnh;|C03. Navier-Stokes Equations(n=2)

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4. Other Equations in Fluid Mechanic水利图书!q&m$H;\.`3r1J

].W*BRC m ^-t}05. Pattern Formation Equations

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N0wg^D6C5z T W06. Dissipative Wave Equations水利图书 ^-d^6UQ%`!J%y*[

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7. The Ginzburg-Landau Equation水利图书6I aa|(s.@4~h l6Q/t$w

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8. Differentiability of the Semigroup

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CHAPTER Ⅶ Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions

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&cfU0tOX6V(W0Introduction水利图书/m"i-oZH9m.]Y;j

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PART A: NoN-WELL-POSED PROBLEMS水利图书F P8kTKx(]

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1. Dissipativity and Well Posedness

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2. Estimate of Dimension for Non-Well-Posed Problems: Examples in Fluid Dynamics

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$VL'xyw$`6^3Co0PART B: UNSTABLE MANIFOLDS, LYAPUNOV FUNCTIONS, AND LOWER BOUNDS ON DIMENSIONS水利图书6k.K ` j2_wDdHj

xl;uNe&C xA,vX03. Stable and Unstable Manifolds

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8I-Q| |E6_K k!l04. The Attractor of a Semigroup with a Lyapunov Function

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5. Lower Bounds on Dimensions of Attractors: An Example

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3`^8|TP Y3w_Rs0CHAPTER Ⅷ The Cone and Squeezing Properties. Inertial Manifolds

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Introduction水利图书Egg"M9VH pl j!`

m-}2{G4fF9S"a_01. The Cone Property水利图书3AT-O9^F,U

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2. Construction of an Inertial Manifold: DeScription of the Method水利图书)I!aTd~

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3. Existence of an Inertial Manifold

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^f/Y6Q {O9b04. Examples

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5. Approximation and Stability of the Inertial Manifold with Respect to Perturbations水利图书I5u#|N!QO ^bg0\

m6cSD?"zp0g0CHAPTER Ⅸ Inertial Manifolds and Slow Manifolds. The Non-Self-Adjoint Case

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Introduction

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)iZ;U9G'om6[+cnp'a01. The Functional Setting水利图书gBW@7wDH,gZ,W

aJ0f)`(\oNC:c02. The Main Result Lipschitz Case

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3. Complements and Applications水利图书};c4tn:G9d M(\#v!c

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4. Inertial Manifolds and Slow Manifolds

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CHAPTER Ⅹ Approximation of Attractors and Inertial Manifolds. Convergent Families of Approximate Inertial Manifolds

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Introduction

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G|x*T-U!K*r*rv01. Construction of the Manifolds

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"II1D$n"F y3v`02. Approximation of Attractors水利图书k3a!Zx%?5Rlh7R

N4[*k.V W9@L0Z03. Convergent Families of Approximate Inertial Manifolds水利图书`m/q%c {'JUeA

7dO2nn-]n'K4_0APPENDIX Collective Sobolev Inequalities水利图书 [8gRHST

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Introduction水利图书 lj.T @ E*G6^%k

uww y9N+vr#]9Z9hv01. Notations and Hypotheses

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Q{;O,^ y/f,Q02. Spectral Estimates for Schrodinger-Type Operators

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$Co]"n(b&]$o03. Generalization of the Sobolev-Lieb-Thirring Inequality Ⅰ水利图书;]5w*G4vh l6V\

Q7W0K1N+?};]M J04. Generalization of the Sobolev-Lieb-Thirring Inequality Ⅱ

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5. Examples

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Bibliography

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