Partial Differential Equations V: Asymptotic Methods for Partial Differential Equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1999
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
34 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution |
| Beschreibung: | 1 Online-Ressource (VII, 247 p) |
| ISBN: | 9783642584237 9783642635861 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-642-58423-7 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042422726 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1999 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642584237 |c Online |9 978-3-642-58423-7 | ||
| 020 | |a 9783642635861 |c Print |9 978-3-642-63586-1 | ||
| 024 | 7 | |a 10.1007/978-3-642-58423-7 |2 doi | |
| 035 | |a (OCoLC)863682586 | ||
| 035 | |a (DE-599)BVBBV042422726 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Fedoryuk, M. V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Partial Differential Equations V |b Asymptotic Methods for Partial Differential Equations |c edited by M. V. Fedoryuk |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1999 | |
| 300 | |a 1 Online-Ressource (VII, 247 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Encyclopaedia of Mathematical Sciences |v 34 |x 0938-0396 | |
| 500 | |a In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Statistical Physics, Dynamical Systems and Complexity | |
| 650 | 4 | |a Mathematik | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-58423-7 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858143 | ||
Datensatz im Suchindex
| _version_ | 1804153097552920576 |
|---|---|
| any_adam_object | |
| author | Fedoryuk, M. V. |
| author_facet | Fedoryuk, M. V. |
| author_role | aut |
| author_sort | Fedoryuk, M. V. |
| author_variant | m v f mv mvf |
| building | Verbundindex |
| bvnumber | BV042422726 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863682586 (DE-599)BVBBV042422726 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-58423-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02931nmm a2200421zcb4500</leader><controlfield tag="001">BV042422726</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1999 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642584237</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-58423-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642635861</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-63586-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-58423-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863682586</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422726</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fedoryuk, M. V.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Partial Differential Equations V</subfield><subfield code="b">Asymptotic Methods for Partial Differential Equations</subfield><subfield code="c">edited by M. V. Fedoryuk</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VII, 247 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Encyclopaedia of Mathematical Sciences</subfield><subfield code="v">34</subfield><subfield code="x">0938-0396</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistical Physics, Dynamical Systems and Complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-58423-7</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858143</subfield></datafield></record></collection> |
| id | DE-604.BV042422726 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642584237 9783642635861 |
| issn | 0938-0396 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858143 |
| oclc_num | 863682586 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VII, 247 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Fedoryuk, M. V. Verfasser aut Partial Differential Equations V Asymptotic Methods for Partial Differential Equations edited by M. V. Fedoryuk Berlin, Heidelberg Springer Berlin Heidelberg 1999 1 Online-Ressource (VII, 247 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 34 0938-0396 In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution Mathematics Global analysis (Mathematics) Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik https://doi.org/10.1007/978-3-642-58423-7 Verlag Volltext |
| spellingShingle | Fedoryuk, M. V. Partial Differential Equations V Asymptotic Methods for Partial Differential Equations Mathematics Global analysis (Mathematics) Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik |
| title | Partial Differential Equations V Asymptotic Methods for Partial Differential Equations |
| title_auth | Partial Differential Equations V Asymptotic Methods for Partial Differential Equations |
| title_exact_search | Partial Differential Equations V Asymptotic Methods for Partial Differential Equations |
| title_full | Partial Differential Equations V Asymptotic Methods for Partial Differential Equations edited by M. V. Fedoryuk |
| title_fullStr | Partial Differential Equations V Asymptotic Methods for Partial Differential Equations edited by M. V. Fedoryuk |
| title_full_unstemmed | Partial Differential Equations V Asymptotic Methods for Partial Differential Equations edited by M. V. Fedoryuk |
| title_short | Partial Differential Equations V |
| title_sort | partial differential equations v asymptotic methods for partial differential equations |
| title_sub | Asymptotic Methods for Partial Differential Equations |
| topic | Mathematics Global analysis (Mathematics) Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik |
| url | https://doi.org/10.1007/978-3-642-58423-7 |
| work_keys_str_mv | AT fedoryukmv partialdifferentialequationsvasymptoticmethodsforpartialdifferentialequations |