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分数阶扩散方程的定性理论(英文版)

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作者慕嘉

出版社科学出版社

ISBN9787030736628

出版时间2022-12

装帧平装

开本16开

定价88元

货号1202785524

上书时间2024-09-04

大智慧小美丽

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Contents

《博士后文库》序言

Preface

Chapter1 Preliminaries 1

1.1 Introduction 1

1.2 Fractionalintegrals and fractional derivatives 3

1.3 Mittag-Leffler functions 5

1.4 Measureof noncompactness 5

1.5 Semigroupsofoperators 6

1.6 Fixedpointtheorems 8

1.7 Definitions of solutions to abstract fractional equations 9

1.8 Other lemmas 11

Chapter2 Initial (or Boundary)Value Problems forFractional Diffusion Equations 13

2.1 Impulsive fractional diffusion equations with nonlocal initial conditions 13

2.1.1 Introduction 13

2.1.2 Existence of mild solutions 16

2.1.3 Examples 21

2.1.4 Notes and remarks 23

2.2 Initial problems for fractional diffusion equations in fractionalpower spaces 23

I2.2.1 ntroduction 23

2.2.2 Existence of q-mild solutions 25

2.2.3 Existence of q-classical solutions 30

2.2.4 Applications 30

2.2.5 Notes and remarks 32

2.3 Positive mild solutionstoperiodicboundaryvalue problemsfor fractional diffusion equations 32 Introduction 32

2.3.1 Contents

2.3.2 Existence of mild solutions 38

2.3.3 Examples 40

2.3.4 Notes and remarks 41

2.4 Periodicboundaryvalue problems for semilinear fractional differential equations 41

2.4.1 Introduction 41

2.4.2 Existence of mild solutions 44

2.4.3 Notes and remarks 51

Chapter3 Bounded Solutions toFractional Diffusion Equations 52

3.1 Bounded solutions to fractional diffusion equations with C0-semigroups 52

3.1.1 Introduction 52

3.1.2 Results for linear equations 59

3.1.3 Results for nonlinear equations 64

3.1.4 Examples 69

3.1.5 Notes and remarks 70

3.2 Periodic (orS-asymptotically) solutions to fractional diffusion equations in fractionalpower spaces 70

3.2.1 Introduction 70

3.2.2 Existenceofperiodic(or S-asymptotically) mild or classical solutions 74

3.2.3 Examples 81

3.2.4 Notes and remarks 82

3.3 Square-mean S-asymptoticallyperiodic solutions to fractional stochastic diffusion equations 82

3.3.1 Introduction 82

3.3.2 Existence-uniqueness of square-mean S-asymptotically !-periodic solutions 88

3.3.3 Asymptotically stabilityof square-mean S-asymptotically !-periodic solutions 98

3.3.4 Examples 99

3.3.5 Notes and remarks 100

Chapter4 Existence and Regularityof Solutions toFractional Diffusion Equations 101

4.1 Existence and regularityof solutions to fractional diffusion equations involving time-dependentdiffusion coefficients 101

4.1.1 Introduction 101

4.1.2 Existence and regularityof classical solutions 107

4.1.3 Notes and remarks 118

4.2 Existence and regularityof solutions to fractional diffusion equations involving time-space-dependent diffusion coefficients 118

4.2.1 Introduction 118

4.2.2 Existence and regularityof classical solutions 121

4.2.3 Notes and remarks 128

Bibliography 129

Index 144

编后记 145

内容摘要
该专著主要包括了分数阶泛函微分方程、分数阶抽象常微分方程、分数阶抽象发展方程、基于临界点理论的分数阶边值问题、分数阶偏微分方程解对初值的连续依赖性、存在性、正则性、专享性、多解性等。该专著主要包括了分数阶泛函微分方程、分数阶抽象常微分方程、分数阶抽象发展方程、基于临界点理论的分数阶边值问题、分数阶偏微分方程解对初值的连续依赖性、存在性、正则性、专享性、多解性等。

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分数阶扩散方程的定性理论(英文版)

大智慧小美丽

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