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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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.e/v0so$l#Z0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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作  者: R.Temam 著水利图书M~J&J:b7s `

K9E!xZ%mJI4GxC7[b0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khCw6R#e2fEs

9Dh$B.}Z0字  数:

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{r.dSqG;Z@ o7X0版  次: 1水利图书;li6a;A.Nulw

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页  数: 648水利图书s:HT4C Yw

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印刷时间:水利图书.d0hIJZ5@-b1}]

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开  本:

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J0{3Y6j-i0印  次:水利图书 |k]9K_.v Mf

zN5W^&Bx'b:Q0纸  张: 胶版纸水利图书 mG~Ay.|

@mv?E0I S B N : 9787506247160

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包  装: 平装

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,C)R.}:m0`g;i?p0所属分类: 图书 >> 自然科学 >> 力学

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jsfCX;o'cb0内容简介水利图书 q\nuGuH

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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.

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目录水利图书 ODj0AQ yG

z4ye}*o}'B4gs0Preface to the Second Edition水利图书K;H\(NG

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Preface to the First Edition水利图书,y'mX%V"cV#cM9? h

w0l;zj1UID3j)@f0GENERAL INTRODUCTION.水利图书6a1}6QV9H Q

U'hyz,s}4Q0The User‘s Guide水利图书2u#sVfm0V1V$Ita

#j*`!|[4A'T'A;Sw0Introduction水利图书H+I$fiy9d9bE

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1. Mechanism and Description of Chaos. The Finite-Dimensional Case水利图书3l GA%b#k%s'HGO

)Z/[-B+~ A0Q jf.z_02. Mechanism and Description of Chaos. The Infinite-Dimensional Case

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3. The Global Attractor. Reduction to Finite Dimension水利图书;?R%T9W1Mu,U Uc

g%f\@U\)EK04. Remarks on the Computational Aspect

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5. The User‘s Guide水利图书?.a&x X#l$a4h tXJ

)s[4p(fy9b0CHAPTER ⅠGeneral Results and Concepts on Invariant Sets and Attractors

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'UUX]9P0Introduction水利图书G0R a$_B

5qT{B'BF.m1ox#b`01. Semigroups, Invariant Sets, and Attractors

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2. Examples in Ordinary Differential Equations

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feN;N/@"|1_:[J03. Fractal Interpolation and Attractors水利图书n)wn7SI.Bu f

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CHAPTERⅡ Elements of Functional Analysis

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Introduction

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P/z;mEcz01. Function Spaces

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2. Linear Operators

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3. Linear Evolution Equations of the First Order in Time水利图书c]5dCw7ME

0UT3c)TZ9Q04. Linear Evolution Equations of the Second Order in Time

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W%e0XG\9hwz0CHAPTER Ⅲ Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction-Diffusion Equations. Fluid Mechanics and Pattern Formation Equations Introduction

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L5MWhTL[(M~01. Reaction-Diffusion Equations水利图书 @9v oVs)D

;M0s7ND C _'J$sl!fZ02. Navier-Stokes Equations(n=2)

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3. Other Equations in Fluid Mechanics水利图书fa8UQd~#L8j

g,i.T\&p*^ ~ Y)r04. Some Pattern Formation Equations水利图书7k!pA6a D [{;N6]}x o

!yN yd#]R05. Semilinear Equations水利图书$}f8? y.o T

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6. Backward Uniqueness

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n3Uz6p1u'P5l~ B0CHAPTER Ⅳ Attractors of Dissipative Wave Equations

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w-_)o|"v*K[s0Introduction

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&lH3F9SH'{f01. Linear Equations: Summary and Additional Results水利图书3W8SNvI

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2. The Sine-Gordon Equation水利图书cnk7M%i7g|

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3. A Nonlinear Wave Equation of Relativistic Quantum Mechanics水利图书0aR!bm3QI"Q

k6e/sfg!U3{04. An Abstract Wave Equation水利图书)PyP+i5rZ3V

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5. The Ginzburg-Landau Equation水利图书n$e G4}g5_&C iG V%P

_%s.H&Z-i0MA6ET06. Weakly Dissipative Equations. I. The Nonlinear Schr6dinger Equation

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3Os)w n'Q'}B.J0e07. Weakly Dissipative Equations II. The Korteweg-De Vries Equation水利图书-HaU.xf-AB

|/D[2l0RS$`08. Unbounded Case: The Lack of Compactness水利图书5TLI4N/BI#ad8x

+u&A!d(f6pDtR8z09. Regularity of Attractors

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10. Stability of Attractors

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CHAPTER Ⅴ Lyapunov Exponents and Dimension of Attractors

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Introduction

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X[ AL*My j01. Linear and Multilinear Algebra水利图书7t9Cp9vgbW

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2. Lyapunov Exponents and Lyapunov Numbers水利图书F9S%Dt(kmW

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3. Hausdorff and Fractal Dimensions of Attractors水利图书2O\8o;AD

D$Y0D-e9K@:Iy0CHAPTER Ⅵ Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems

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Introduction水利图书Mb(DRB'S/G/u]xY

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1. The Lorenz Attractor水利图书p pe!O?b#@4c

*lAOc6m} u02. Reaction-Diffusion Equations水利图书"^TM8DZ Oi

4m t5]&Zf03. Navier-Stokes Equations(n=2)

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4. Other Equations in Fluid Mechanic水利图书7H.R._%P.P7d&{fp#g

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5. Pattern Formation Equations水利图书x/~j9~3j `+}*b7IW

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6. Dissipative Wave Equations水利图书5v5WW9G['j@Z

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7. The Ginzburg-Landau Equation

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y$g~9g)q.qr08. Differentiability of the Semigroup

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coxH ZGj0CHAPTER Ⅶ Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions水利图书0^2r,N o-fzX XE

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Introduction

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VV*L'EL'bBC^%B.Vh G0PART A: NoN-WELL-POSED PROBLEMS水利图书9h.b&E)iJ wL8@0@$b{

e5Wozv01. 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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l(ZPQ&c:d%K([0PART B: UNSTABLE MANIFOLDS, LYAPUNOV FUNCTIONS, AND LOWER BOUNDS ON DIMENSIONS

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3. Stable and Unstable Manifolds

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6i8ObgX*o04. The Attractor of a Semigroup with a Lyapunov Function水利图书~g6Vp8RN}8y.r

K.f BA#M]L05. Lower Bounds on Dimensions of Attractors: An Example水利图书{y(J U2U8p'T#gC+O O

z&`$De2wr\y0CHAPTER Ⅷ The Cone and Squeezing Properties. Inertial Manifolds水利图书h:fN3}~-s,X

.Y7O)F#a7^X R/N sPq0Introduction

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(A7`*jN@L01. The Cone Property水利图书@rz1K1r5Ww}

)qg/^~A02. Construction of an Inertial Manifold: DeScription of the Method水利图书 l/eh:{s @c1}

.H}VOn#R.L8}?'p(n2`W03. Existence of an Inertial Manifold水利图书0ip A`}S0_"bC2p{

%kp?z1p\_ P5Q04. Examples水利图书uE"}5CL6zvn7MR/h

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5. Approximation and Stability of the Inertial Manifold with Respect to Perturbations

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8L;Acv)}kK0CHAPTER Ⅸ Inertial Manifolds and Slow Manifolds. The Non-Self-Adjoint Case

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Introduction

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r4? EI;_1i;|[P01. The Functional Setting水利图书IQGJ3g`!S

4u|v*ly02. The Main Result Lipschitz Case

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3. Complements and Applications

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;^F0hz:[9? @E04. Inertial Manifolds and Slow Manifolds

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CHAPTER Ⅹ Approximation of Attractors and Inertial Manifolds. Convergent Families of Approximate Inertial Manifolds水利图书1Of qw*rD:p*F-[[

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Introduction水利图书 }"\v#Q-k h E8x

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1. Construction of the Manifolds水利图书|W Tx1S6U2}'U

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2. Approximation of Attractors水利图书0nE/Nj5Ys zI5U

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3. Convergent Families of Approximate Inertial Manifolds

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APPENDIX Collective Sobolev Inequalities水利图书3wP0z8oyC:? ?

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Introduction

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1. Notations and Hypotheses水利图书o.G]6@i Xr

&XM%N_4NlLo02. Spectral Estimates for Schrodinger-Type Operators水利图书'V UM-d'S(\k?

8aO~ o'H-Kt-x&[03. Generalization of the Sobolev-Lieb-Thirring Inequality Ⅰ

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v6A&jrL8Fvdw B%Kp04. Generalization of the Sobolev-Lieb-Thirring Inequality Ⅱ水利图书0mJ+Fl5kqu

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5. Examples

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