Evolution equations arising in the modelling of life sciences:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2013
|
| Schriftenreihe: | International series of numerical mathematics
163 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 217 S. graph. Darst. |
| ISBN: | 9783034806145 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
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| 003 | DE-604 | ||
| 005 | 20130529 | ||
| 007 | t | ||
| 008 | 130409s2013 d||| |||| 00||| eng d | ||
| 020 | |a 9783034806145 |9 978-3-0348-0614-5 | ||
| 035 | |a (OCoLC)844051496 | ||
| 035 | |a (DE-599)BVBBV040933159 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-355 |a DE-11 | ||
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| 100 | 1 | |a Efendiev, Messoud |d 1953- |e Verfasser |0 (DE-588)1048410544 |4 aut | |
| 245 | 1 | 0 | |a Evolution equations arising in the modelling of life sciences |c Messoud Efendiev |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2013 | |
| 300 | |a XII, 217 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of numerical mathematics |v 163 | |
| 650 | 0 | 7 | |a Evolutionsgleichung |0 (DE-588)4129061-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Biomathematik |0 (DE-588)4139408-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |2 gnd |9 rswk-swf |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-0348-0615-2 |
| 830 | 0 | |a International series of numerical mathematics |v 163 |w (DE-604)BV035415862 |9 163 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025912071 | ||
Datensatz im Suchindex
| _version_ | 1804150232700682240 |
|---|---|
| adam_text | Contents
Auxiliary
Materials............................ 1
1.1
Functional
Spaces
and Embedding
Theorems............ 1
1.2
Linear Elliptic Boundary Value Problems
.............. 4
1.3
Nemytskii Operator
......................... 8
Global Attractors for Autonomous Evolution Equations
....... 17
2.1
Kolmogorov
ε
-Entropy and Its Asymptotics in Functional Spaces
. 17
2.2
Global Attractors and Finite-Dimensional Reduction
........ 19
Verifying Life Science Models Containing Diffusion, Transport and
Interaction of Species
........................... 25
3.1 Semilinear
Autonomous Case
.................... 26
3.2 Quasilinear
Autonomous Case
.................... 30
3.3
Fully Nonlinear Autonomous Case
................. 52
Positivity
Criterion for Systems of Stochastic PDEs
.......... 59
4.1
Positivity
and Stochastic Perturbation of
Semilinear
Parabolic
Systems: The Simplest Case
..................... 59
4.2
Positivity
Criterion for
Semilinear
RDS: Non-
autonomous Case
. . 65
4.3
Wong-Zakaï
Approximation and Random Systems of PDEs
.... 73
4.4
Stochastic PDE Case
......................... 76
4.5
Necessary and Sufficient Conditions for Comparison Principles:
Stochastic Case
........................... 82
Existence and Longtime Behaviour of
a Biofilm
Model
........ 87
5.1
Single-Species/Single-Substrate
Biofilm
Model
.......... 87
5.2
A Bioclogging Model That Accounts for Spatial Spreading of
Bacteria
...............................
Ill
5.3
Antibiotic Disinfections of
Biofilms
................. 129
5.4
Amensalistic
Biofilm
Control System
................ 155
5.5
Mathematical Model of Quorum Sensing in Patchy
Biofilm
Communities
............................. 167
xii Contents
6
The Blood Coagulation Cascade in
a Perfusion
Experiment:
Example from the Pharmaceutical Industry
..............195
6.1
A Reaction-Diffusion-Advection Model for the Blood Coagulation
Cascade
...............................196
6.2
Numerical Simulations Without Adhesion of Platelets
.......199
References
...................................209
Index
......................................215
This book deals with the modeling, analysis and simulation of problems arising in the
life sciences, and especially in biological processes. The models and findings presented
result from intensive discussions with microbiologists, doctors and medical staff, physi¬
cists, chemists and industrial engineers and are based on experimental data. They lead
to a new class of degenerate density-dependent nonlinear reaction-diffusion convective
equations that simultaneously comprise two kinds of degeneracy: porous-medium and
fast-diffusion type degeneracy. To date, this class is still not clearly understood in the
mathematical literature and thus is especially interesting.
The author derives both realistic life science models and their governing equations which
are of the above-mentioned degenerate types, and systematically studies these classes
of equations. In each concrete case, well-posedness, the dependence of solutions on
boundary conditions reflecting some properties of the environment, and the large-time
behavior of solutions are investigated and, in some instances, also studied numerically.
|
| any_adam_object | 1 |
| author | Efendiev, Messoud 1953- |
| author_GND | (DE-588)1048410544 |
| author_facet | Efendiev, Messoud 1953- |
| author_role | aut |
| author_sort | Efendiev, Messoud 1953- |
| author_variant | m e me |
| building | Verbundindex |
| bvnumber | BV040933159 |
| classification_rvk | SK 950 WC 7000 |
| ctrlnum | (OCoLC)844051496 (DE-599)BVBBV040933159 |
| dewey-full | 570.15153534 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 570 - Biology |
| dewey-raw | 570.15153534 |
| dewey-search | 570.15153534 |
| dewey-sort | 3570.15153534 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| format | Book |
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| id | DE-604.BV040933159 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:35:39Z |
| institution | BVB |
| isbn | 9783034806145 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025912071 |
| oclc_num | 844051496 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-11 |
| physical | XII, 217 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Birkhäuser |
| record_format | marc |
| series | International series of numerical mathematics |
| series2 | International series of numerical mathematics |
| spelling | Efendiev, Messoud 1953- Verfasser (DE-588)1048410544 aut Evolution equations arising in the modelling of life sciences Messoud Efendiev Basel [u.a.] Birkhäuser 2013 XII, 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of numerical mathematics 163 Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Biomathematik (DE-588)4139408-2 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-0348-0615-2 International series of numerical mathematics 163 (DE-604)BV035415862 163 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025912071&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025912071&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Efendiev, Messoud 1953- Evolution equations arising in the modelling of life sciences International series of numerical mathematics Evolutionsgleichung (DE-588)4129061-6 gnd Biomathematik (DE-588)4139408-2 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4139408-2 (DE-588)7651795-0 |
| title | Evolution equations arising in the modelling of life sciences |
| title_auth | Evolution equations arising in the modelling of life sciences |
| title_exact_search | Evolution equations arising in the modelling of life sciences |
| title_full | Evolution equations arising in the modelling of life sciences Messoud Efendiev |
| title_fullStr | Evolution equations arising in the modelling of life sciences Messoud Efendiev |
| title_full_unstemmed | Evolution equations arising in the modelling of life sciences Messoud Efendiev |
| title_short | Evolution equations arising in the modelling of life sciences |
| title_sort | evolution equations arising in the modelling of life sciences |
| topic | Evolutionsgleichung (DE-588)4129061-6 gnd Biomathematik (DE-588)4139408-2 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Evolutionsgleichung Biomathematik Mathematische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025912071&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025912071&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415862 |
| work_keys_str_mv | AT efendievmessoud evolutionequationsarisinginthemodellingoflifesciences |