Methods of small parameter in mathematical biology:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Birkhäuser
2014
|
| Schriftenreihe: | Modeling and simulation in science, engineering and technology
|
| Online-Zugang: | DE-634 DE-861 DE-91 DE-384 DE-19 DE-703 DE-20 DE-739 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783319051406 |
| DOI: | 10.1007/978-3-319-05140-6 |
Internformat
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Datensatz im Suchindex
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METHODS OF SMALL PARAMETER IN MATHEMATICAL BIOLOGY
/ BANASIAK, JACEK
: 2014
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1 SMALL PARAMETER METHODS – BASIC IDEAS
2 INTRODUCTION TO THE CHAPMAN–ENSKOG METHOD – LINEAR MODELS WITH
MIGRATIONS
3 TIKHONOV–VASILYEVA THEORY
4 THE TIKHONOV THEOREM IN SOME MODELS OF MATHEMATICAL BIOSCIENCES
5 ASYMPTOTIC EXPANSION METHOD IN A SINGULARLY PERTURBED MCKENDRICK
PROBLEM
6 DIFFUSION LIMIT OF THE TELEGRAPH EQUATION
7 KINETIC MODEL OF ALIGNMENT
8 FROM MICROSCOPIC TO MACROSCOPIC DESCRIPTIONS. - 9 CONCLUSION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
METHODS OF SMALL PARAMETER IN MATHEMATICAL BIOLOGY
/ BANASIAK, JACEK
: 2014
ABSTRACT / INHALTSTEXT
THIS MONOGRAPH PRESENTS NEW TOOLS FOR MODELING MULTISCALE BIOLOGICAL
PROCESSES. NATURAL PROCESSES ARE USUALLY DRIVEN BY MECHANISMS WIDELY
DIFFERING FROM EACH OTHER IN THE TIME OR SPACE SCALE AT WHICH THEY
OPERATE AND THUS SHOULD BE DESCRIBED BY APPROPRIATE MULTISCALE MODELS.
HOWEVER, LOOKING AT ALL SUCH SCALES SIMULTANEOUSLY IS OFTEN INFEASIBLE,
COSTLY, AND PROVIDES INFORMATION THAT IS REDUNDANT FOR A PARTICULAR
APPLICATION. HENCE, THERE HAS BEEN A GROWING INTEREST IN PROVIDING A
MORE FOCUSED DESCRIPTION OF MULTISCALE PROCESSES BY AGGREGATING
VARIABLES IN A WAY THAT IS RELEVANT AND PRESERVES THE SALIENT FEATURES
OF THE DYNAMICS. THE AIM OF THIS BOOK IS TO PRESENT A SYSTEMATIC WAY OF
DERIVING THE SO-CALLED LIMIT EQUATIONS FOR SUCH AGGREGATED VARIABLES AND
ENSURING THAT THE COEFFICIENTS OF THESE EQUATIONS ENCAPSULATE THE
RELEVANT INFORMATION FROM THE DISCARDED LEVELS OF DESCRIPTION.SINCE ANY
APPROXIMATION IS ONLY VALID IF AN ESTIMATE OF THE INCURRED ERROR IS
AVAILABLE, THE TOOLS DESCRIBED ALLOW FOR PROVING THAT THE SOLUTIONS TO
THE ORIGINAL MULTISCALE FAMILY OF EQUATIONS CONVERGE TO THE SOLUTION OF
THE LIMIT EQUATION IF THE RELEVANT PARAMETER CONVERGES TO ITS CRITICAL
VALUE. THE CHAPTERS ARE ARRANGED ACCORDING TO THE MATHEMATICAL
COMPLEXITY OF THE ANALYSIS, FROM SYSTEMS OF ORDINARY LINEAR DIFFERENTIAL
EQUATIONS, THROUGH NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS, TO LINEAR
AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS. MANY CHAPTERS BEGIN WITH A
SURVEY OF MATHEMATICAL TECHNIQUES NEEDED FOR THE ANALYSIS. ALL PROBLEMS
DISCUSSED IN THIS BOOK BELONG TO THE CLASS OF SINGULARLY PERTURBED
PROBLEMS; THAT IS, PROBLEMS IN WHICH THE STRUCTURE OF THE LIMIT EQUATION
IS SIGNIFICANTLY DIFFERENT FROM THAT OF THE MULTISCALE MODEL. SUCH
PROBLEMS APPEAR IN ALL AREAS OF SCIENCE AND CAN BE ATTACKED USING MANY
TECHNIQUES. METHODS OF SMALL PARAMETER IN MATHEMATICAL BIOLOGY WILL
APPEAL TO SENIOR UNDERGRADUATE AND GRADUATE STUDENTS IN APPLED AND
BIOMATHEMATICS, AS WELL AS RESEARCHERS SPECIALIZING IN DIFFERENTIAL
EQUATIONS AND ASYMPTOTIC ANALYSIS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. |
| any_adam_object | 1 |
| author | Banasiak, Jacek 1959- Lachowicz, Mirosław |
| author_GND | (DE-588)141516585 (DE-588)1058418297 |
| author_facet | Banasiak, Jacek 1959- Lachowicz, Mirosław |
| author_role | aut aut |
| author_sort | Banasiak, Jacek 1959- |
| author_variant | j b jb m l ml |
| building | Verbundindex |
| bvnumber | BV041866146 |
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| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Biologie Mathematik |
| doi_str_mv | 10.1007/978-3-319-05140-6 |
| format | Electronic eBook |
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| spelling | Banasiak, Jacek 1959- Verfasser (DE-588)141516585 aut Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz Cham [u.a.] Birkhäuser 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Modeling and simulation in science, engineering and technology Lachowicz, Mirosław Verfasser (DE-588)1058418297 aut Erscheint auch als Druckausgabe 978-3-319-05139-0 https://doi.org/10.1007/978-3-319-05140-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027310334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027310334&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Banasiak, Jacek 1959- Lachowicz, Mirosław Methods of small parameter in mathematical biology |
| title | Methods of small parameter in mathematical biology |
| title_auth | Methods of small parameter in mathematical biology |
| title_exact_search | Methods of small parameter in mathematical biology |
| title_full | Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz |
| title_fullStr | Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz |
| title_full_unstemmed | Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz |
| title_short | Methods of small parameter in mathematical biology |
| title_sort | methods of small parameter in mathematical biology |
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