Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120522-1096725-1-2 Inhaltsverzeichnis |
| Physical Description: | VII, 176 S. graph. Darst. |
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
LIST O F FIGURES III
LIST O F SYMBOLS V
INTRODUCTION 1
1. MATHEMATICAL MODELLING O F BIOFILMS 9
1.1. PROTOTYPE BIOFILM GROWTH MODEL 11
1.1.1. MATHEMATICAL MODEL 11
1.1.2. ANALYTICAL RESULTS 13
1.2. MULTICOMPONENT BIOFILM MODELS 15
1.2.1. ANTIBIOTIC DISINFECTION OF BIOFILMS 15
1.2.2. QUORUM-SENSING IN PATCHY BIOFILM COMMUNITIES 17
1.3. WELL-POSEDNESS OF THE QUORUM-SENSING MODEL 19
1.3.1. PRELIMINARIES 19
1.3.2. UNIQUENESS 22
1.3.3. EXISTENCE 24
1.3.4. NUMERICAL SIMULATIONS 32
1.4. CONCLUDING REMARKS 38
2. VERIFYING MATHEMATICAL MODELS 3 9
2.1. POSITIVITY CRITERIA FOR DETERMINISTIC SYSTEMS 41
2.1.1. SEMI-LINEAR SYSTEMS 41
2.1.2. QUASI-LINEAR SYSTEMS 43
2.2. COMPARISON PRINCIPLES FOR DETERMINISTIC SYSTEMS 52
2.2.1. SEMI-LINEAR SYSTEMS 53
2.2.2. QUASI-LINEAR SYSTEMS 55
2.3. GENERALIZATIONS AND APPLICATIONS 63
2.3.1. OTHER BOUNDARY VALUES 64
2.3.2. POSITIVITY PROPERTY OF DETERMINISTIC MODELS 65
2.4. STOCHASTIC PERTURBATIONS OF DETERMINISTIC SYSTEMS 69
2.4.1. MOTIVATION: ADDITIVE VERSUS MULTIPLICATIVE NOISE 69
2.4.2. STOCHASTIC PERTURBATIONS OF SEMI-LINEAR PARABOLIC SYSTEMS 74
2.4.3. A POSITIVITY CRITERION FOR NON-AUTONOMOUS DETERMINISTIC SYSTEMS .
75 2.5. STOCHASTIC SYSTEMS: POSITIVITY PROPERTY AND COMPARISON
PRINCIPLES . . . . 80 2.5.1. RANDOM APPROXIMATIONS OF STOCHASTIC SYSTEMS
80
HTTP://D-NB.INFO/1032386789
IMAGE 2
CONTENTS
2.5.2. A POSITIVITY CRITERION FOR STOCHASTIC SYSTEMS 83
2.5.3. COMPARISON PRINCIPLES FOR STOCHASTIC SYSTEMS 86
2.5.4. VERIFYING STOCHASTIC MODELS 89
2.6. CONCLUDING REMARKS 90
3. EXPONENTIAL ATTRACTORS O F INFINITE DIMENSIONAL DYNAMICAL SYSTEMS 9 3
3.1. AUTONOMOUS EVOLUTION EQUATIONS 95
3.1.1. SEMIGROUPS AND GLOBAL ATTRACTORS 95
3.1.2. ON THE DIMENSION OF ATTRACTORS 97
3.1.3. EXPONENTIAL ATTRACTORS OF SEMIGROUPS 99
3.1.4. EXISTENCE RESULTS FOR EXPONENTIAL ATTRACTORS 102
THE DISCRETE CASE 104
THE TIME CONTINUOUS CASE 109
3.1.5. CONSEQUENCES OF THE CONSTRUCTION AND PROPERTIES OF THE
EXPONENTIAL ATTRACTOR 113
3.2. NON-AUTONOMOUS EVOLUTION EQUATIONS 120
3.2.1. EVOLUTION PROCESSES AND NON-AUTONOMOUS GLOBAL ATTRACTORS . . . .
120 3.2.2. PREVIOUS RESULTS: EXISTENCE OF GLOBAL AND EXPONENTIAL
PULLBACK AT TRACTORS 125
3.2.3. EXISTENCE RESULTS FOR PULLBACK EXPONENTIAL ATTRACTORS 129
THE DISCRETE CASE 131
THE TIME CONTINUOUS CASE 137
3.2.4. CONSEQUENCES OF THE CONSTRUCTION AND PROPERTIES OF THE PULLBACK
EXPONENTIAL ATTRACTOR 138
3.2.5. APPLICATIONS 149
NON-AUTONOMOUS CHAFEE-INFANTE EQUATION 150
NON-AUTONOMOUS DAMPED WAVE EQUATION 155
3.3. CONCLUDING REMARKS 163
A. FUNCTION SPACES 165
B. AN AUXILIARY LEMMA 169
BIBLIOGRAPHY 171
II
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| discipline | Biologie Mathematik |
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| language | English |
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| physical | VII, 176 S. graph. Darst. |
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| spelling | Sonner, Stefanie Verfasser aut Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions Stefanie Sonner 2012 VII, 176 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Biofilm (DE-588)4232790-8 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Biofilm (DE-588)4232790-8 s Mathematische Modellierung (DE-588)7651795-0 s Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20120522-1096725-1-2 http://mediatum.ub.tum.de/node?id=1096725 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120522-1096725-1-2 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025089205&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sonner, Stefanie Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions Biofilm (DE-588)4232790-8 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 gnd |
| subject_GND | (DE-588)4232790-8 (DE-588)7651795-0 (DE-588)4253347-8 (DE-588)4113937-9 |
| title | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions |
| title_auth | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions |
| title_exact_search | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions |
| title_full | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions Stefanie Sonner |
| title_fullStr | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions Stefanie Sonner |
| title_full_unstemmed | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions Stefanie Sonner |
| title_short | Systems of quasi-linear PDEs arising in the modelling of biofilms and related dynamical questions |
| title_sort | systems of quasi linear pdes arising in the modelling of biofilms and related dynamical questions |
| topic | Biofilm (DE-588)4232790-8 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 gnd |
| topic_facet | Biofilm Mathematische Modellierung Quasilineare parabolische Differentialgleichung Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1096725 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120522-1096725-1-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025089205&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sonnerstefanie systemsofquasilinearpdesarisinginthemodellingofbiofilmsandrelateddynamicalquestions |