中图网(原中国图书网):网上书店,中文字幕在线一区二区三区,尾货特色书店,中文字幕在线一区,30万种特价书低至2折!

歡迎光臨中圖網 請 | 注冊
> >
非線性自治動力系統的吸引子(英文)

包郵 非線性自治動力系統的吸引子(英文)

作者:秦玉明
出版社:科學出版社出版時間:2022-07-01
開本: B5 頁數: 224
本類榜單:自然科學銷量榜
中 圖 價:¥102.4(8.0折) 定價  ¥128.0 登錄后可看到會員價
加入購物車 收藏
開年大促, 全場包郵
?新疆、西藏除外
本類五星書更多>

非線性自治動力系統的吸引子(英文) 版權信息

  • ISBN:9787030702500
  • 條形碼:9787030702500 ; 978-7-03-070250-0
  • 裝幀:一般膠版紙
  • 冊數:暫無
  • 重量:暫無
  • 所屬分類:>

非線性自治動力系統的吸引子(英文) 內容簡介

Thisbookisbasedonthefirstauthor''''slecture"Infinite-dimensionaldynamicalsystemsonnonlinearautonomoussystems"tobegiventograduatestudentsinDonghuaUniversitysince2004.Itisaimedatpresentingcompleteandsystematictheoriesofinfinite-dimensionaldynamicalsystemsandtheirapplicationsinpartialdifferentialequations,espelyinthemodelsoffluidmechanics.Thisbookaimstopresentsomerecentresultsonsomeautonomousnonlinearevolutionaryequationsaarisingfromphysics,fluidmechanicsandmaterialsciencesuchastheNavier-Stokesequations,Navier-Stokes-Voightsystems,thenonlinearthermoviscoelasticsystem,etc.Mostofmaterialsofthisbookarebasedontheresearchcarriedoutbytheauthorsinrecentyears.Someofthemhadbeenpreviouslypublishedonlyinoriginalpapers,andsomeofthematerialhaveneverbeenpublisheduntilnow.

非線性自治動力系統的吸引子(英文) 目錄

Contents
Preface i
CHAPTER 1
Preliminary 1
1.1 Some Useful Inequalities 1
1.2 Basic Theory of Infinite-Dimensional Dynamical Systems for Autonomous Nonlinear Evolutionary Equations 10
1.2.1 Uniformly Compact Semigroups 10
1.2.2 Weakly Compact Semigroups 16
1.2.3 Q-Limit Compact Semigroups 17
1.2.4 Asymptotically Compact Semigroups 22
1.2.5 Asymptotically Smooth Semigroups 27
1.2.6 Norm-to-Weak Continuous Semigroups 28
1.2.7 Closed Operator Semigroups 30
1.3 Basic Theory of Finite-Dimensional Attractors 32
1.3.1 The Fractal Dimension of Global Attractors 32
1.3.2 The Estimate on Fractal Dimension of Global Attractors 33
CHAPTER 2 Global Attractors for the Navier-Stokes-Voight Equations with Delay 37
2.1 Global Wellposedness of Solutions 37
2.2 Existence of Global Attractors 43
2.2.1 Dissipation: Existence of Absorbing Sets 43
2.2.2 Asymptotical Compactness and Existence of Attractor 44
2.3 Bibliographic Comments 46
CHAPTER 3 Global Attractor and Its Upper Estimate on Fractal Dimension for the 2D Navier-Stokes-Voight Equations 47
3.1 Global Existence of Solutions 47
3.2 Existence of Global Attractors 55
3.2.1 Existence of Absorbing Sets 55
3.2.2 Some Compactness and the Existence of Global Attractors 56
3.3 Upper Estimate on the Fractal Dimension of Global Attractors 58
3.4 Bibliographic Comments 64
CHAPTER 4 Maximal Attractor for the Equations of One-Dimensional Compressible Polytropic Viscous Ideal Gas 67
41 Our Problem 67
4.2 Nonlinear Semigroup on 69
4.3 Existence of an Absorbing Set in 73
4.4 Existence of an Absorbing Set in 83
4.5 Proof of Theorem 4.2.1 86
4.6 Bibliographic Comments 88
CHAPTER 5 Universal Attractors for a Nonlinear System of Compressible One-Dimensional Heat-Conducting Viscous Real Gas 91
5.1 Main Results 91
5.2 Nonlinear Co-Semigroup on 95
5.3 Existence of an Absorbing Set in 97
5.4 Existence of an Absorbing Set in 106
5.5 Proof of Theorem 5.1.1 108
5.6 Bibliographic Comments 111
CHAPTER 6 Global Attractors for the Compressible Navier-Stokes Equations in Bounded Annular Domains 115
6.1 Main Result 115
6.2 Nonlinear Semigroup on 119
6.3 Existence of an Absorbing Set in 120
6.4 Existence of an Absorbing Set in 129
6.5 Existence of an Absorbing Set in 135
6.6 Bibliographic Comments 146
CHAPTER 7 Global Attractor for a Nonlinear Thermoviscoelastic System in Shape Memory Alloys 149
7.1 Main Result 149
7.2 An Absorbing Set in Hs 152
7.3 Compactness of the Orbit in Hs 165
7.4 Bibliographic Comments 173
CHAPTER 8 Global Attractors for Nonlinear Reaction-Diffusion Equations and the 2D Navier-Stokes Equations 175
8.1 Global Attractor for Strong Solutions of Reaction-Diffusion Equations 175
8.1.1 Existence of Solutions and Uniqueness 176
8.1.2 Global Attractor for the Semigroup in 176
8.1.3 Global Attractor of System in and 177
8.2 Global Attractors for the 2D Navier-Stokes Equations in 183
CHAPTER 9 Global Attractors for an Incompressible Fluid Equation and a Wave Equation 187
9.1 An Incompressible Fluid Equation 187
9.2 A Wave Equation with Nonlinear Damping 193
9.2.1 Wellposedness of Solutions 194
9.2.2 Dissipativity 196
9.2.3 Asymptotic Compactness and Existence of Global Attractor 200
References 203
Index 211
展開全部

非線性自治動力系統的吸引子(英文) 節選

Chapter 1 Preliminary In this chapter, we shall recall some basic knowledge in functional analysis (harmonic analysis) and idds for nonlinear evolutionary equations, most of which will be used in the subsequent chapters. The reader can easily find the detailed proofs in the related literature, see, e.g., Adams [1], Babin and Vishik [5],Chemin [20],Chepyzhov and Vishik [24], Constantin and Foias [27],Evans [30],Hale [54], Hille and Phillips [57], Kato [93],Ladyzhenskaya [74,75],Lemarie-Rieusse [76], Lions [78], Liu and Zheng [81], Lorentz [82],Liu and Zheng [80],Maz,ja [89],Miao [90, 91], Nirenberg [97], Novotny and Strauskraba [98], Pazy [104], Qin [112], Robinson [125], Rudin [126], Sell and You [129], Serrin [130], Smoller [135], Sobolev [136], Sogge [137],Sohr [138], Stein [141], Temam, Babin and Vishik [5],Sell and You [129], Temam [144-146], Triebel [147,148], Walter [150], Yosida [155],Zheng [156, 157], Zhongj Fan and Chen [161],etc. 1.1 Some Useful Inequalities In this section, we shall recall some inequalities which will be used in the subsequent chapters. Throughout next chapters, we set, C will stand for a generic positive constant, depending on Q and some constants, but independent of the choice of the initial time and t. We introduce the Hausdorff semi-distance in X between two sets and. We set, divu, H is the closure of the set E infe topology, V is the closure of the set E in topology, W is the closure of the set E in (H2(Q))k topology, i.e., (1.1.1) (1.1.2) P is the Helmholz-Leray orthogonal projection in onto the space is the Stokes operator subject to the nonslip homogeneous Dirichlet boundary condition with the domain,and A is a self-adjoint positively defined operator on H. is a compact operator from H to H. The sequence {cOj}^ is an orthonormal system of eigenfunctions of are the eigenvalues of the Stokes operator A corresponding to the eigenfunctions Let (1-1.3) where is a Hilbert space, and. Clearly, Vo = H, and ,Hf and are dual spaces of H and V respectively, where the injection is dense, continuous. denote the norm and inner product of H, respectively, i.e., (1.1.4) and denote the norm and inner product in V, respectively, i.e., (1.1.5) and (1.1.6) The norm denotes the norm in denotes the dual product in V and Vf. We define the following bilinear form operator: (1.1.7) and the trilinear form operator (1.1.8) dxi and (1.1.9) where A is defined as, for all. Clearly, the trilinear operator satisfies (1.1.10) (1.1.11) (1.1.12) (1.1.13) (1.1.14) Here, if the Hq norm and Hq norm replace V norm and W norm, respectively, the above inequalities also hold. There exists a positive constant C depending only on Q such that. Theorem 1.1.1 (Young,s Inequality). The following inequalities hold pecially, Theorem 1.1.2 (The Cauchy-Schwarz Inequality). There holds that, for all x G Rn. (1.1.15) (1.1.16) (1.1.17) (1.1.18) Theorem 1.1.3 (Holder Inequality). Let QC]Rn be a domain,assume that and. (1.1.19) Theorem 1.1.4 (Minkowski5s Inequality). Assume cxd. Then for any, (1.1.20) Attractors for Nonlinear Autonomous Dynamical Systems Theorem 1.1.5 (Jensen,s Inequality with Integration). Let g(x) be a function defined on (a, b) and a 0 and m> 0. Let now be given. Suppose that the map is continuously differentiable and fulfills the differential inequality for some e > 0 and k > 0. Theorem 1.1.10 (Gronwall,s Inequality), Let be an absolutely continuous function satisfying at where e > 0,,for all t>s>0 and some m > 0. Under assumptions of theorem 1.1.6, the following inequalities hold for dimension n = 3. Theorem 1.1.11 (Ladyzhenskaya、Inequality). (1.1.25) (1.1.26) Theorem 1.1.12 (Sobolev’s Inequality). Assume that Q Ca bounded smooth domain,then for dimension n = 3, there holds (1.1.27) Theorem 1.1.13 (The Gagliardo-Nirenberg Inequality). (1.1.28) (1.1.29) The

商品評論(0條)
暫無評論……
書友推薦
本類暢銷
編輯推薦
返回頂部
中圖網
在線客服
主站蜘蛛池模板: 黄石东方妇产医院_黄石妇科医院哪家好_黄石无痛人流医院 | 北京晚会活动策划|北京节目录制后期剪辑|北京演播厅出租租赁-北京龙视星光文化传媒有限公司 | 塑料异型材_PVC异型材_封边条生产厂家_PC灯罩_防撞扶手_医院扶手价格_东莞市怡美塑胶制品有限公司 | 汽车水泵_汽车水泵厂家-瑞安市骏迪汽车配件有限公司 | 高柔性拖链电缆_卷筒电缆_耐磨耐折聚氨酯电缆-玖泰特种电缆 | 江门流水线|江门工作台|江门市伟涛行工业设备有限公司 | 多功能三相相位伏安表-变压器短路阻抗测试仪-上海妙定电气 | 杭州月嫂技术培训服务公司-催乳师培训中心报名费用-产后康复师培训机构-杭州优贝姆健康管理有限公司 | 分类168信息网 - 分类信息网 免费发布与查询 | 小程序开发公司_APP开发多少钱_软件开发定制_微信小程序制作_客户销售管理软件-济南小溪畅流网络科技有限公司 | 郑州外墙清洗_郑州玻璃幕墙清洗_郑州开荒保洁-河南三恒清洗服务有限公司 | 空调风机,低噪声离心式通风机,不锈钢防爆风机,前倾皮带传动风机,后倾空调风机-山东捷风风机有限公司 | 驾驶式洗地机/扫地机_全自动洗地机_工业洗地机_荣事达工厂官网 | 自动气象站_气象站监测设备_全自动气象站设备_雨量监测站-山东风途物联网 | 通辽信息港 - 免费发布房产、招聘、求职、二手、商铺等信息 www.tlxxg.net | TPE_TPE热塑性弹性体_TPE原料价格_TPE材料厂家-惠州市中塑王塑胶制品公司- 中塑王塑胶制品有限公司 | PO膜_灌浆膜及地膜供应厂家 - 青州市鲁谊塑料厂 | 破碎机_上海破碎机_破碎机设备_破碎机厂家-上海山卓重工机械有限公司 | 苏州柯瑞德货架-仓库自动化改造解决方案| 水热合成反应釜-防爆高压消解罐-西安常仪仪器设备有限公司 | 不锈钢管件(不锈钢弯头,不锈钢三通,不锈钢大小头),不锈钢法兰「厂家」-浙江志通管阀 | 健康管理师报名入口,2025年健康管理师考试时间信息网-网站首页 塑料造粒机「厂家直销」-莱州鑫瑞迪机械有限公司 | 全自动包衣机-无菌分装隔离器-浙江迦南科技股份有限公司 | 选矿设备,选矿生产线,选矿工艺,选矿技术-昆明昆重矿山机械 | 杭州标识标牌|文化墙|展厅|导视|户内外广告|发光字|灯箱|铭阳制作公司 - 杭州标识标牌|文化墙|展厅|导视|户内外广告|发光字|灯箱|铭阳制作公司 | 锻造液压机,粉末冶金,拉伸,坩埚成型液压机定制生产厂家-山东威力重工官方网站 | 玻璃钢型材-玻璃钢风管-玻璃钢管道,生产厂家-[江苏欧升玻璃钢制造有限公司] | 昊宇水工|河北昊宇水工机械工程有限公司 | 广东泵阀展|阀门展-广东国际泵管阀展览会 | 长江船运_国内海运_内贸船运_大件海运|运输_船舶运输价格_钢材船运_内河运输_风电甲板船_游艇运输_航运货代电话_上海交航船运 | 济南菜鸟驿站广告|青岛快递车车体|社区媒体-抖音|墙体广告-山东揽胜广告传媒有限公司 | SMC-SMC电磁阀-日本SMC气缸-SMC气动元件展示网 | 铝合金线槽_铝型材加工_空调挡水板厂家-江阴炜福金属制品有限公司 | 矿用履带式平板车|探水钻机|气动架柱式钻机|架柱式液压回转钻机|履带式钻机-启睿探水钻机厂家 | ALC墙板_ALC轻质隔墙板_隔音防火墙板_轻质隔墙材料-湖北博悦佳 | 机床导轨_导轨板_滚轮导轨-上海旻佑精密机械有限公司 | 酒水灌装机-白酒灌装机-酒精果酒酱油醋灌装设备_青州惠联灌装机械 | 自动螺旋上料机厂家价格-斗式提升机定制-螺杆绞龙输送机-杰凯上料机 | 膏剂灌装旋盖机-眼药水灌装生产线-西林瓶粉剂分装机-南通博琅机械科技 | 电线电缆厂家|沈阳电缆厂|电线厂|沈阳英联塑力线缆有限公司 | 双工位钻铣攻牙机-转换工作台钻攻中心-钻铣攻牙机一体机-浙江利硕自动化设备有限公司 |