Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Shaker
2000
|
| Schriftenreihe: | Berichte aus der Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Darmstadt, Techn. Univ., Diss., 2000 |
| Beschreibung: | II, 102 S. graph. Darst. : 21 cm |
| ISBN: | 3826581822 |
Internformat
MARC
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| 044 | |a gw |c DE | ||
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| 100 | 1 | |a Mark, Jürgen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods |c Jürgen Mark |
| 264 | 1 | |a Aachen |b Shaker |c 2000 | |
| 300 | |a II, 102 S. |b graph. Darst. : 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Mathematik | |
| 500 | |a Zugl.: Darmstadt, Techn. Univ., Diss., 2000 | ||
| 650 | 0 | 7 | |a Wiener-Hopf-Faktorisierung |0 (DE-588)4128926-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Viskoelastizität |0 (DE-588)4063621-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Cauchy-Anfangswertproblem |0 (DE-588)4147404-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Anfangsrandwertproblem |0 (DE-588)4001990-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Viskoelastizität |0 (DE-588)4063621-5 |D s |
| 689 | 0 | 1 | |a Cauchy-Anfangswertproblem |0 (DE-588)4147404-1 |D s |
| 689 | 0 | 2 | |a Anfangsrandwertproblem |0 (DE-588)4001990-1 |D s |
| 689 | 0 | 3 | |a Wiener-Hopf-Faktorisierung |0 (DE-588)4128926-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009204932&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009204932 | |
Datensatz im Suchindex
| _version_ | 1816443884952092672 |
|---|---|
| adam_text |
CONTENTS
1
LINEAR
VISCOELASTICITY
THEORY
1
1.1
FUNDAMENTAL
RELATIONS
.
1
1.2
LINEAR
VISCOELASTIC
STRESS-STRAIN
RELATIONS
.
3
1.3
ISOTROPIC,
HOMOGENEOUS
CONTINUA
.
5
2
THE
SCALAR
CAUCHY
PROBLEM
7
2.1
DISTRIBUTIONAL
SETTING
IN
(X)
.
8
2.1.1
DISTRIBUTIONAL
EQUATION
OF
MOTION
.
8
2.1.2
DEFINITION
OF
THE
FUNDAMENTAL
RESOLVENT
.
10
2.1.3
EXPONENTIAL
GROWTH
AND
FOURIER-LAPLACE
TRANSFORMATION
.
12
2.1.4
STRUCTURE
OF
THE
FUNDAMENTAL
RESOLVENT
.
14
2.1.5
STRICT
SOLUTION
OF
THE
ABSTRACT
CAUCHY
PROBLEM
.
17
2.2
THE
CASE
OF
A
HILBERT
SPACE
X
=
H
.
18
2.2.1
WEAK
FORMULATION
OF
THE
EQUATION
OF
MOTION
.
18
2.2.2
EXPONENTIAL
DECAY
AND
A-PRIORI
ESTIMATES
.
21
2.3
THE
CASE
OF
TEMPERED
DISTRIBUTIONS
X
=
S'
(R
3
)
.
23
2.3.1
PARAMETER-DEPENDENT
HELMHOLTZ
EQUATION
.
23
2.3.2
EXPLICIT
FUNDAMENTAL
DISPLACEMENT
DISTRIBUTION
.
25
2.3.3
EXPLICIT
SOLUTION
OF
THE
SCALAR
CAUCHY
PROBLEM
.
26
3
SCALAR
INITIAL-BOUNDARY
VALUE
PROBLEMS
29
3.1
DISTRIBUTIONAL
AND
WEAK
FORMULATIONS
.
30
3.2
PARAMETER-DEPENDENT
ELLIPTIC
PROBLEMS
.
32
3.3
EXPLICIT
REPRESENTATION
FORMULAS
.
34
3.3.1
INHOMOGENEOUS
INITIAL
VALUE
PROBLEMS
.
34
3.3.2
HOMOGENEOUS
BOUNDARY
VALUE
PROBLEMS
.
36
II
CONTENTS
4
VECTORIAL
INITIAL-BOUNDARY
VALUE
PROBLEMS
41
4.1
THE
VECTORIAL
CAUCHY
PROBLEM
.
41
4.1,1
DISTRIBUTIONAL
EQUATIONS
OF
MOTION
.
41
4.1.2
HELMHOLTZ
DECOMPOSITION
AND
DISPLACEMENT
POTENTIALS
.
43
4.1.3
EXPONENTIAL
GROWTH
AND
FOURIER-LAPLACE
TRANSFORMATION
.
45
4.1.4
EXPLICIT
FUNDAMENTAL
DISPLACEMENT
TENSOR
.
46
4.1.5
EXPLICIT
SOLUTION
OF
THE
VECTORIAL
CAUCHY
PROBLEM
.
48
4.2
HALF-SPACE
PROBLEMS
.
49
4.2.1
CANONICAL
PROBLEM
FORMULATIONS
.
49
4.2.2
EXPLICIT
SOLUTION
OF
THE
INITIAL
VALUE
PROBLEM
.
51
4.2.3
EXPLICIT
SOLUTION
OF
THE
BOUNDARY
VALUE
PROBLEM
.
52
4.3
HALF-PLANE
CRACK
PROBLEMS
.
57
4.3.1
PROBLEM
FORMULATIONS
AND
TRANSMISSION
CONDITIONS
.
57
4.3.2
EQUIVALENT
WIENER-HOPF
OPERATORS
.
61
4.3.3
EXPLICIT
WIENER-HOPF
FACTORIZATIONS
FOR
MODEL
PROBLEMS
.
65
A
MATERIAL
FUNCTIONS
71
A.L
CREEP
FUNCTIONS
.
71
A.
1.1
GENERAL
FUNCTION
CLASSES
.
71
A.
1.2
PROPERTIES
OF
THE
LAPLACE-STIELTJES
TRANSFORMS
.
73
A.
1.3
COMPLETELY
POSITIVE
MEASURES
.
75
A.
2
CLASSIFICATION
OF
MATERIALS
.
76
A.
2.1
SCALAR
STRESS-STRAIN
RELATION
.
76
A.
2.2
INSTANTANEOUS
AND
LONGTERM
MATERIAL
BEHAVIOUR
.
77
A.
2.3
VISCOUS
FLUID
.
77
A.
2.4
RIGID
FLUID
.
79
A.
2.5
RIGID
SOLID
.
81
A.
2.6
VISCOUS
SOLID
.
82
B
THE
LAPLACE
OPERATOR
85
B.L
THE
LAPLACE
OPERATOR
IN
A
BANACH
SPACE
SETTING
.
85
C
SOBOLEV
SPACES
87
C.L
CLASSICAL
DEFINITIONS
OF
SOBOLEV
SPACES
.
87
C.L.L
WEIGHTED
SOBOLEV
SPACES
.
89
C.L.
2
ANISOTROPIC,
WEIGHTED
SOBOLEV
SPACES
.
91
D
COMPLEX
METHODS
95
D.L
BOUNDARY
VALUES
OF
ANALYTIC
FUNCTIONS
.
95
D.2
WIENER-HOPF
FACTORIZATIONS
.
97 |
| any_adam_object | 1 |
| author | Mark, Jürgen |
| author_facet | Mark, Jürgen |
| author_role | aut |
| author_sort | Mark, Jürgen |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013485946 |
| illustrated | Illustrated |
| indexdate | 2024-11-22T17:17:59Z |
| institution | BVB |
| isbn | 3826581822 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009204932 |
| oclc_num | 50129555 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | II, 102 S. graph. Darst. : 21 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Shaker |
| record_format | marc |
| series2 | Berichte aus der Mathematik |
| spelling | Mark, Jürgen Verfasser aut Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods Jürgen Mark Aachen Shaker 2000 II, 102 S. graph. Darst. : 21 cm txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mathematik Zugl.: Darmstadt, Techn. Univ., Diss., 2000 Wiener-Hopf-Faktorisierung (DE-588)4128926-2 gnd rswk-swf Viskoelastizität (DE-588)4063621-5 gnd rswk-swf Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd rswk-swf Anfangsrandwertproblem (DE-588)4001990-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Viskoelastizität (DE-588)4063621-5 s Cauchy-Anfangswertproblem (DE-588)4147404-1 s Anfangsrandwertproblem (DE-588)4001990-1 s Wiener-Hopf-Faktorisierung (DE-588)4128926-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009204932&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mark, Jürgen Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods Wiener-Hopf-Faktorisierung (DE-588)4128926-2 gnd Viskoelastizität (DE-588)4063621-5 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Anfangsrandwertproblem (DE-588)4001990-1 gnd |
| subject_GND | (DE-588)4128926-2 (DE-588)4063621-5 (DE-588)4147404-1 (DE-588)4001990-1 (DE-588)4113937-9 |
| title | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods |
| title_auth | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods |
| title_exact_search | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods |
| title_full | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods Jürgen Mark |
| title_fullStr | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods Jürgen Mark |
| title_full_unstemmed | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods Jürgen Mark |
| title_short | Initial boundary value problems in linear viscoelasticity using Wiener-Hopf methods |
| title_sort | initial boundary value problems in linear viscoelasticity using wiener hopf methods |
| topic | Wiener-Hopf-Faktorisierung (DE-588)4128926-2 gnd Viskoelastizität (DE-588)4063621-5 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Anfangsrandwertproblem (DE-588)4001990-1 gnd |
| topic_facet | Wiener-Hopf-Faktorisierung Viskoelastizität Cauchy-Anfangswertproblem Anfangsrandwertproblem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009204932&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT markjurgen initialboundaryvalueproblemsinlinearviscoelasticityusingwienerhopfmethods |