Linear and quasilinear parabolic problems: 1 Abstract linear theory
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1995
|
| Series: | Monographs in mathematics
89 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXV, 335 S. |
| ISBN: | 3764351144 0817651144 |
Staff View
MARC
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| 245 | 1 | 0 | |a Linear and quasilinear parabolic problems |n 1 |p Abstract linear theory |c Herbert Amann |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1995 | |
| 300 | |a XXXV, 335 S. | ||
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| 490 | 1 | |a Monographs in mathematics |v 89 | |
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Record in the Search Index
| _version_ | 1804124691987693568 |
|---|---|
| adam_text | Contents
Preface
......................................
vii
Introduction
.................................. xiii
Notations and Conventions
1
Topologica!
Spaces
............................ 1
2
Locally Convex Spaces
.......................... 2
3
Complexifications
............................ 4
4
Unbounded Linear Operators
...................... 6
5
General Conventions
........................... 7
Chapter I Generators and Interpolation
1
Generators of Analytic Semigroups
1.1
Properties of Linear Operators
..................... 10
1.2
The Class
H(Ei,E0)
........................... 11
1.3
Perturbation Theorems
......................... 14
1-4
Spectral Estimates
............................ 15
1.5
Compact Perturbations
......................... 20
1.6
Matrix Generators
............................ 21
2
Interpolation Functors
2.1
Definitions
................................ 24
2.2
Interpolation Inequalities
........................ 25
2.3
Retractions
................................ 26
2.4
Standard Interpolation Functors
.................... 28
2.5
Continuous Injections
.......................... 30
2.6
Duality Properties
............................ 30
2.7
Compactness
............................... 31
2.8
Reiteration Theorems
.......................... 31
2.9
Fractional Powers and Interpolation
.................. 32
2.10
Semigroups and Interpolation
...................... 33
2.11
Admissible Interpolation Functors
................... 35
v Contents
Chapter II Cauchy Problems and Evolution Operators
1
Linear Cauchy Problems
1.1
Holder Spaces
..............................
40
1.2
Existence and Regularity Theorems
.................. 43
2
Parabolic Evolution Operators
2.1
Basic Properties
.............................
45
2.2
Determining Integral Equations
..................... 47
3
Linear Volterra Integral Equations
3.1
Weakly Singular Kernels
......................... 48
3.2
Resolvent Kernels
............................
50
3.3
Singular Gronwall Inequalities
..................... 52
4
Existence of Evolution Operators
4.1
A Class of Parameter Integrals
..................... 53
4.2
Semigroup Estimates
.......................... 55
4.3
Construction of Evolution Operators
.................. 57
4.4
The Main Result
............................. 63
4.5
Solvability of the Cauchy Problem
................... 66
5
Stability Estimates
5.1
Estimates for Evolution Operators
................... 68
5.2
Continuity Properties of Mild Solutions
................ 71
5.3
Holder Estimates
............................. 72
5.4
Boundedness of Mild Solutions
..................... 74
6
Invariance
and
Positivity
6.1
Yosida Approximations
......................... 75
6.2
Approximations of Evolution Operators
................ 77
6.3
Invariance
................................. 80
6.4
Orderings
and
Positivity.........................
84
Chapter III Maximal Regularity
1
General Principles
1.1
Sobolev Spaces
.............................. 88
1.2
Absolutely Continuous Functions
.................... 89
1.3
Generalized Solutions
.......................... 91
1.4
Trace Spaces
............................... 92
1.5
Pairs of Maximal Regularity
...................... 94
1.6
Stability
.................................. 96
Contents xi
2 Maximal
Holder Regularity
2.1 Singular Holder Spaces ......................... 98
2.2
Semigroup Estimates ..........................
102
2.3
Trace
Spaces............................... 106
2.4
Estimates for KA
............................. 109
2.5
Maximal Regularity
........................... 113
2.6
Nonautonomous Problems
........................ 117
3
Maximal Continuous Regularity
3.1
Necessary Conditions
.......................... 121
3.2
Higher Order Interpolation Spaces
................... 123
3.3
Estimates for KA
............................. 124
3.4
Maximal Regularity
........................... 126
4
Maximal Sobolev Regularity
4.1
Temperate Distributions
......................... 128
4.2
Fourier Transforms and Convolutions
................. 130
4.3
The Hubert Transform
.......................... 135
4.4
UMD Spaces and Fourier Multipliers
.................. 141
4.5
Properties of UMD Spaces
....................... 144
4.6
Fractional Powers
............................ 147
4.7
Bounded Imaginary Powers
....................... 162
4.8
Perturbation Theorems
......................... 168
4.9
Sums of Closed Operators
........................ 173
4.10
Maximal Regularity
........................... 180
Chapter IV Variable Domains
1
Higher Regularity
1.1
Properties of Differentiable Functions
................. 194
1.2
General Solvability Results for Cauchy Problems
........... 195
1.3
Estimates for Evolution Operators
................... 198
1.4
Evolution Operators on Interpolation Spaces
............. 204
1.5
The Cauchy Problem
.......................... 207
2
Constant Interpolation Spaces
2.1
Semigroup and Convergence Estimates
................. 211
2.2
Assumptions and Consequences
..................... 214
2.3
Construction of Evolution Operators
.................. 218
2.4
Estimates for Evolution Operators
................... 227
2.5
The Cauchy Problem
.......................... 230
2.6
Abstract Boundary Value Problems
.................. 233
xii
Contents
3
Maximal Regularity
3.1
Abstract Initial Boundary Value Problems
.............. 242
3.2
Isomorphism Theorems
......................... 245
Chapter V Scales of Banach Spaces
1
Banach Scales
1.1
General Concepts
............................ 250
1.2
Power Scales
............................... 255
1.3
Extrapolation Spaces
.......................... 261
1.4
Dual Scales
................................ 267
1.5
Interpolation-Extrapolation Scales
................... 275
2
Evolution Equations in Banach Scales
2.1
Semigroups in Interpolation-Extrapolation Scales
........... 286
2.2
Parabolic Evolution Equations in Banach Scales
........... 294
2.3
Duality
.................................. 297
2.4
Approximation Theorems
........................ 300
2.5
Final Value Problems
.......................... 304
2.6
Weak Solutions and Duality
....................... 307
2.7
Positivity
................................. 312
2.8
General Evolution Equations
...................... 314
Bibliography
.................................. 321
List of Symbols
................................ 329
Index
....................................... 333
|
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| id | DE-604.BV010275931 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:49:42Z |
| institution | BVB |
| isbn | 3764351144 0817651144 |
| language | English |
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| physical | XXXV, 335 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Amann, Herbert 1938- Verfasser (DE-588)106045687 aut Linear and quasilinear parabolic problems 1 Abstract linear theory Herbert Amann Basel [u.a.] Birkhäuser 1995 XXXV, 335 S. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 89 Monographs in mathematics ... Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Parabolische Differentialgleichung (DE-588)4173245-5 s DE-604 (DE-604)BV010275930 1 Monographs in mathematics 89 (DE-604)BV000008284 89 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006836756&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Amann, Herbert 1938- Linear and quasilinear parabolic problems Monographs in mathematics Evolutionsgleichung (DE-588)4129061-6 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4173245-5 |
| title | Linear and quasilinear parabolic problems |
| title_auth | Linear and quasilinear parabolic problems |
| title_exact_search | Linear and quasilinear parabolic problems |
| title_full | Linear and quasilinear parabolic problems 1 Abstract linear theory Herbert Amann |
| title_fullStr | Linear and quasilinear parabolic problems 1 Abstract linear theory Herbert Amann |
| title_full_unstemmed | Linear and quasilinear parabolic problems 1 Abstract linear theory Herbert Amann |
| title_short | Linear and quasilinear parabolic problems |
| title_sort | linear and quasilinear parabolic problems abstract linear theory |
| topic | Evolutionsgleichung (DE-588)4129061-6 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Evolutionsgleichung Parabolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006836756&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT amannherbert linearandquasilinearparabolicproblems1 |