Holdings: Phase separation coupled with damage processes

Phase separation coupled with damage processes: analysis of phase field models in elastic media

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Bibliographic Details
Main Authors:	Heinemann, Christian (Author), Kraus, Christiane (Author)
Format:	Thesis Book
Language:	English
Published:	Wiesbaden Springer Spektrum 2014
Subjects:	Cahn-Hilliard-Gleichung System von partiellen Differentialgleichungen Schadensmechanik Elastischer Werkstoff Entmischung Hochschulschrift
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	XII, 172 S. Ill.
ISBN:	9783658052515

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MARC


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Record in the Search Index

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adam_text	CONTENTS 1 INTRODUCTION 1 2 MATHEMATICAL PRELIMINARIES 9 2.1 NOTATION 10 2.2 VECTOR MEASURES AND VECTOR-VALUED FUNCTIONS OF BOUNDED VARIATIONS . 12 2.3 VARIATIONAL METHODS 15 2.3.1 T-CONVERGENCE 15 2.3.2 EMBEDDING THEOREMS AND INEQUALITIES 16 2.3.3 APPROXIMATIONS OF W LSP (Q) AND L Q {0.T: W 1,P (FT))-FUNCTIONS . . 20 2.3.4 CHARACTERIZATION OF CERTAIN VARIATIONAL INEQUALITIES 26 2.4 SHRINKING SETS AND ADMISSIBLE SUBSETS 28 2.4.1 COVERING AND REPRESENTATION RESULTS 29 2.4.2 LOCAL SOBOLEV SPACES ON SHRINKING SETS 33 3 PDE MODELING AND THERMODYNAMIC CONSISTENCY 35 3.1 PHASE SEPARATION AND COARSENING PROCESSES 36 3.2 PARTIAL DAMAGE PROCESSES 40 3.3 COMPLETE DAMAGE PROCESSES 44 3.4 PHASE SEPARATION COUPLED WITH DAMAGE PROCESSES 47 4 CAHN-HILLIARD SYSTEMS WITH POLYNOMIAL CHEMICAL POTENTIALS COUPLED WITH DAMAGE PROCESSES AND HOMOGENEOUS ELASTICITY 51 4.1 ASSUMPTIONS 52 4.2 WEAK FORMULATIONS AND EXISTENCE RESULTS 54 HTTP://D-NB.INFO/1047504588 CONTENTS 4.2.1 REGULARIZATION 55 4.2.2 LIMIT PROBLEM 60 4.3 PROOFS OF THE EXISTENCE THEOREMS 61 4.3.1 EXISTENCE OF WEAK SOLUTIONS FOR THE REGULARIZED SYSTEM 61 4.3.2 EXISTENCE OF WEAK SOLUTIONS FOR THE LIMIT SYSTEM 83 5 CAHN-HILLIARD SYSTEMS WITH LOGARITHMIC CHEMICAL POTENTIALS COUPLED WITH DAMAGE PROCESSES AND INHOMOGENEOUS ELASTICITY 91 5.1 ASSUMPTIONS 92 5.2 WEAK FORMULATIONS AND EXISTENCE RESULTS 93 5.3 PROOFS OF THE EXISTENCE THEOREMS 98 5.3.1 EXISTENCE OF WEAK SOLUTIONS FOR THE REGULARIZED SYSTEM 98 5.3.2 EXISTENCE OF WEAK SOLUTIONS FOR THE LIMIT SYSTEM - POLYNOMIAL CASE 107 5.3.3 HIGHER INTEGRABILITY OF THE STRAIN TENSOR 110 5.3.4 EXISTENCE OF WEAK SOLUTIONS FOR THE LIMIT SYSTEM - LOGARITHMIC CASE 115 6 COMPLETE DAMAGE PROCESSES 119 6.1 ASSUMPTIONS 120 6.2 WEAK FORMULATIONS AND EXISTENCE RESULTS 120 6.3 PROOFS OF THE EXISTENCE THEOREMS 126 6.3.1 T-LIMIT OF THE REGULARIZED ENERGY 126 6.3.2 DEGENERATE LIMIT OF THE REGULARIZED SYSTEM 131 6.3.3 LOCAL- AND GLOBAL-IN-TIME EXISTENCE RESULTS 138 7 CAHN-HILLIARD SYSTEMS COUPLED WITH COMPLETE DAMAGE PROCESSES AND HOMOGENEOUS ELASTICITY 145 7.1 ASSUMPTIONS 146 7.2 WEAK FORMULATIONS AND EXISTENCE RESULTS 147 7.3 PROOFS OF THE EXISTENCE THEOREMS 150 7.3.1 F-LIMIT OF THE REGULARIZED ENERGY 150 7.3.2 DEGENERATE LIMIT OF THE REGULARIZED SYSTEM 152 7.3.3 LOCAL- AND GLOBAL-IN-TIME EXISTENCE RESULTS 160 8 CONCLUSION 163 REFERENCES 167 LIST OF FIGURES 173
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author	Heinemann, Christian Kraus, Christiane
author_facet	Heinemann, Christian Kraus, Christiane
author_role	aut aut
author_sort	Heinemann, Christian
author_variant	c h ch c k ck
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ctrlnum	(OCoLC)881858229 (DE-599)DNB1047504588
dewey-full	531.38201515353
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	531 - Classical mechanics
dewey-raw	531.38201515353
dewey-search	531.38201515353
dewey-sort	3531.38201515353
dewey-tens	530 - Physics
discipline	Physik Mathematik Werkstoffwissenschaften / Fertigungstechnik
format	Thesis Book
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spelling	Heinemann, Christian Verfasser aut Phase separation coupled with damage processes analysis of phase field models in elastic media Christian Heinemann ; Christiane Kraus Wiesbaden Springer Spektrum 2014 XII, 172 S. Ill. txt rdacontent n rdamedia nc rdacarrier Zugl.: Berlin, Humboldt-Univ., Diss., 2013 Cahn-Hilliard-Gleichung (DE-588)4723055-1 gnd rswk-swf System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd rswk-swf Schadensmechanik (DE-588)4194956-0 gnd rswk-swf Elastischer Werkstoff (DE-588)4151686-2 gnd rswk-swf Entmischung (DE-588)4152371-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Elastischer Werkstoff (DE-588)4151686-2 s Schadensmechanik (DE-588)4194956-0 s Entmischung (DE-588)4152371-4 s System von partiellen Differentialgleichungen (DE-588)4116672-3 s Cahn-Hilliard-Gleichung (DE-588)4723055-1 s DE-604 Kraus, Christiane Verfasser aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4593970&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027238565&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Heinemann, Christian Kraus, Christiane Phase separation coupled with damage processes analysis of phase field models in elastic media Cahn-Hilliard-Gleichung (DE-588)4723055-1 gnd System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Schadensmechanik (DE-588)4194956-0 gnd Elastischer Werkstoff (DE-588)4151686-2 gnd Entmischung (DE-588)4152371-4 gnd
subject_GND	(DE-588)4723055-1 (DE-588)4116672-3 (DE-588)4194956-0 (DE-588)4151686-2 (DE-588)4152371-4 (DE-588)4113937-9
title	Phase separation coupled with damage processes analysis of phase field models in elastic media
title_auth	Phase separation coupled with damage processes analysis of phase field models in elastic media
title_exact_search	Phase separation coupled with damage processes analysis of phase field models in elastic media
title_full	Phase separation coupled with damage processes analysis of phase field models in elastic media Christian Heinemann ; Christiane Kraus
title_fullStr	Phase separation coupled with damage processes analysis of phase field models in elastic media Christian Heinemann ; Christiane Kraus
title_full_unstemmed	Phase separation coupled with damage processes analysis of phase field models in elastic media Christian Heinemann ; Christiane Kraus
title_short	Phase separation coupled with damage processes
title_sort	phase separation coupled with damage processes analysis of phase field models in elastic media
title_sub	analysis of phase field models in elastic media
topic	Cahn-Hilliard-Gleichung (DE-588)4723055-1 gnd System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Schadensmechanik (DE-588)4194956-0 gnd Elastischer Werkstoff (DE-588)4151686-2 gnd Entmischung (DE-588)4152371-4 gnd
topic_facet	Cahn-Hilliard-Gleichung System von partiellen Differentialgleichungen Schadensmechanik Elastischer Werkstoff Entmischung Hochschulschrift
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