Why the boundary of a round drop becomes a curve of order four:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1992]
|
| Series: | University lecture series
Volume 3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 72 Seiten Diagramme |
| ISBN: | 0821870025 9780821870020 |
Staff View
MARC
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| 240 | 1 | 0 | |a Počemu granica krugloj kapli prevraščaecja v inversnyj obraz ẹllipsa? |
| 245 | 1 | 0 | |a Why the boundary of a round drop becomes a curve of order four |c A. N. Varchenko ; P. I. Etingof |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1992] | |
| 264 | 4 | |c © 1992 | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1. Mathematical model 1
1.1. Filtration flow of an incompressible fluid 1
1.2. The moving boundary problem 2
2. First integrals of boundary motion 5
2.1. Richardson s integrability theorem 5
2.2. Reconstruction of a domain from the values of its moments, and the
inverse problem of two dimensional potential theory 6
2.3. Results on the uniqueness of a domain with given moments (potential) 7
2.4. The result of injection does not depend on the order of work of the
sources and sinks 9
Problems 10
3. Algebraic solutions 11
3.1. Algebraic and abelian domains 11
3.2. Algebraic solutions 11
3.3. The Cauchy transform and its properties 12
3.4. Singularity correspondence theorem 12
3.5. Proof of the theorem on algebraic solutions 14
3.6. Construction of algebraic solutions 14
iii
iv CONTENTS
3.7. Examples 16
Problems 18
4. Contraction of a gas bubble 21
4.1. Formulation of the problem 21
4.2. The inclusion property 22
4.3. Contraction of a convex domain 23
4.4. Contraction points 24
4.5. An analogue of Richardson s theorem 25
4.6. Dynamics of the gravity potential 27
4.7. The gravity potential as the solution of a boundary value problem . 27
4.8. Proof of the main theorem 28
4.9. Self similar solutions 29
4.10. Asymptotics of contraction 30
4.11. Several sources 31
Problems 32
5. Evolution of a multiply connected domain 35
5.1. Statement of the problem 35
5.2. Integrals of motion 35
5.3. Algebraic solutions 36
5.4. Riemann s theorem 37
5.5. Singularity correspondence 38
5.6. Proof of the theorem on algebraic solutions 39
5.7. Construction of solutions . 39
5.8. Reconstruction of an annular domain from its moments 40
Problems 42
CONTENTS v
6. Evolution with topological transformations 43
6.1. Weak solutions of the evolution problem 43
6.2. The simplest algebraic solutions 46
6.3. Weak solutions of the contraction problem 50
6.4. A sufficient condition of a breakup of a symmetric domain 51
Problems 52
7. Contraction problem on surfaces 55
7.1. Physical motivation 55
7.2. Potential and contraction points 55
7.3. Calculation of the generalized gravity potential on the surface .... 56
7.4. Breakup of the boundary on symmetric surfaces of revolution .... 58
Problems 60
Answers and clues to the problems 61
A few open questions 69
References 71
|
| any_adam_object | 1 |
| author | Varčenko, Aleksandr N. 1949- Etingof, Pavel 1969- |
| author_GND | (DE-588)115203257 (DE-588)133258858 |
| author_facet | Varčenko, Aleksandr N. 1949- Etingof, Pavel 1969- |
| author_role | aut aut |
| author_sort | Varčenko, Aleksandr N. 1949- |
| author_variant | a n v an anv p e pe |
| building | Verbundindex |
| bvnumber | BV007722024 |
| classification_rvk | SI 165 SK 520 |
| ctrlnum | (OCoLC)231505737 (DE-599)BVBBV007722024 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007722024 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:08:22Z |
| institution | BVB |
| isbn | 0821870025 9780821870020 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005074337 |
| oclc_num | 231505737 |
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| owner_facet | DE-12 DE-355 DE-BY-UBR DE-739 DE-29T DE-11 DE-91G DE-BY-TUM |
| physical | viii, 72 Seiten Diagramme |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Varčenko, Aleksandr N. 1949- Verfasser (DE-588)115203257 aut Počemu granica krugloj kapli prevraščaecja v inversnyj obraz ẹllipsa? Why the boundary of a round drop becomes a curve of order four A. N. Varchenko ; P. I. Etingof Providence, Rhode Island American Mathematical Society [1992] © 1992 viii, 72 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 3 Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Freies Randwertproblem (DE-588)4155303-2 gnd rswk-swf Fluid (DE-588)4017690-3 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Tropfen (DE-588)4130676-4 gnd rswk-swf Tropfen (DE-588)4130676-4 s Fluid (DE-588)4017690-3 s Strömungsmechanik (DE-588)4077970-1 s Elliptisches Randwertproblem (DE-588)4193399-0 s DE-604 Hydrodynamik (DE-588)4026302-2 s Freies Randwertproblem (DE-588)4155303-2 s Etingof, Pavel 1969- Verfasser (DE-588)133258858 aut Erscheint auch als Online-Ausgabe 978-0-8218-3218-9 University lecture series Volume 3 (DE-604)BV004153846 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005074337&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Varčenko, Aleksandr N. 1949- Etingof, Pavel 1969- Why the boundary of a round drop becomes a curve of order four University lecture series Elliptisches Randwertproblem (DE-588)4193399-0 gnd Freies Randwertproblem (DE-588)4155303-2 gnd Fluid (DE-588)4017690-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd Hydrodynamik (DE-588)4026302-2 gnd Tropfen (DE-588)4130676-4 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4155303-2 (DE-588)4017690-3 (DE-588)4077970-1 (DE-588)4026302-2 (DE-588)4130676-4 |
| title | Why the boundary of a round drop becomes a curve of order four |
| title_alt | Počemu granica krugloj kapli prevraščaecja v inversnyj obraz ẹllipsa? |
| title_auth | Why the boundary of a round drop becomes a curve of order four |
| title_exact_search | Why the boundary of a round drop becomes a curve of order four |
| title_full | Why the boundary of a round drop becomes a curve of order four A. N. Varchenko ; P. I. Etingof |
| title_fullStr | Why the boundary of a round drop becomes a curve of order four A. N. Varchenko ; P. I. Etingof |
| title_full_unstemmed | Why the boundary of a round drop becomes a curve of order four A. N. Varchenko ; P. I. Etingof |
| title_short | Why the boundary of a round drop becomes a curve of order four |
| title_sort | why the boundary of a round drop becomes a curve of order four |
| topic | Elliptisches Randwertproblem (DE-588)4193399-0 gnd Freies Randwertproblem (DE-588)4155303-2 gnd Fluid (DE-588)4017690-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd Hydrodynamik (DE-588)4026302-2 gnd Tropfen (DE-588)4130676-4 gnd |
| topic_facet | Elliptisches Randwertproblem Freies Randwertproblem Fluid Strömungsmechanik Hydrodynamik Tropfen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005074337&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
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