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$ 459 | 分數階擴散方程的定性理論(英文版)
作者：慕嘉 出版社：科學出版社 出版日期：2022-12-01 語言：簡體中文 規格：平裝 / 143頁 / 19 x 26 x 1 cm / 普通級/ 1-1  博客來 - 數學
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圖書名稱：分數階擴散方程的定性理論(英文版)
內容簡介
本書主要介紹分數階擴散方程解的存在性、正則性和穩定性。本書的主要內容來自作者近年來的研究成果，分為四章。第一章介紹了分數階微積分、非線性分析和運算元半群等基本知識。第二章介紹了一些分數階擴散方程初值（或邊值）問題解的存在性結果。第三章的主要目的是介紹分數階擴散方程有界解（如週期解）的存在性。第四章研究分數自治（或非自治）擴散方程解的存在性和正則性。
目錄
Contents
《博士後文庫》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
編後記 145
《博士後文庫》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
編後記 145
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