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分数阶扩散方程的定理论(英文版) 英文原版书慕嘉新华正版

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作者慕嘉

出版社科学出版社

ISBN9787030736628

出版时间2022-12

版次1

装帧平装

开本16

页数164页

字数200千字

定价88元

货号xhwx_1202785524

上书时间2024-12-16

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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 nonpactness 5

1.5 semigrouofoperators 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 estence 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 estence of q-mild solutions 25

2.2.3 estence of q-classical solutions 30

2.2.4 applications 30

2.2.5 notes and remarks 32

2.3 itive mild solutionstoperiodicboundaryvalue problemsfor fractional diffusion equations 32 introduction 32

2.3.1 contents

2.3.2 estence 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 estence 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-semigrou 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 estenceofperiodic(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 estence-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 estence and regularityof solutions tofractional diffusion equations 101

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

4.1.1 introduction 101

4.1.2 estence and regularityof classical solutions 107

4.1.3 notes and remarks 118

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

4.2.1 introduction 118

4.2.2 estence and regularityof classical solutions 121

4.2.3 notes and remarks 128

bibliography 129

index 144

编后记 145

内容简介：

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、存在、正则、、多解等。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、存在、正则、、多解等。