An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients

Pfaff equations with continuous coefficients are considered. A specific Cauchy problem for a Pfaff equation is transformed to an equivalent system of integral equations of a special type, which is overdetermined. It is shown that in the case of smooth coefficients the consistency of the system is eq...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2022-08, Vol.317 (Suppl 1), p.S16-S26
Main Authors: Azamov, A. A., Begaliev, A. O.
Format: Article
Language:English
Subjects:
Cauchy problems
Coefficients
Equivalence
Existence theorems
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Pfaff equation
Uniqueness theorems
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c198t-4fd1aaf41b907aaa0bf813efa7f595cd14e2db706a2c64612661a00c08e7245a3
container_end_page S26
container_issue Suppl 1
container_start_page S16
container_title Proceedings of the Steklov Institute of Mathematics
container_volume 317
creator Azamov, A. A.
Begaliev, A. O.
description Pfaff equations with continuous coefficients are considered. A specific Cauchy problem for a Pfaff equation is transformed to an equivalent system of integral equations of a special type, which is overdetermined. It is shown that in the case of smooth coefficients the consistency of the system is equivalent to the Frobenius integrability criterion. A theorem on the existence of a solution for the obtained type of integral equations is presented. The solution is found by the Euler polygonal method, which allows one to construct an approximate solution of the Pfaff equation. An analog of Nagumo’s theorem on the uniqueness of the solution to the Cauchy problem is also given.
doi_str_mv 10.1134/S0081543822030026
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2736325929</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2736325929</sourcerecordid><originalsourceid>FETCH-LOGICAL-c198t-4fd1aaf41b907aaa0bf813efa7f595cd14e2db706a2c64612661a00c08e7245a3</originalsourceid><addsrcrecordid>eNp1UEtLAzEQDqJgrf4AbwHPq5Pn7h5LqQ-oKLSel3Q3sSlt0iZZrP_e1AoexMMwA99jZj6ErgncEsL43QygIoKzilJgAFSeoAERjBSVBHGKBge4OODn6CLGFQAXJa8HyI4cnuxtTNq1Gs-X2ge9wcp1ufBouw1-bzcqaTzz6z5Z7_CzTkvfYeMDVvjVKGPwZNerb-zDpiUee5es630f86iNsa3VLsVLdGbUOuqrnz5Eb_eT-fixmL48PI1H06IldZUKbjqilOFkUUOplIKFqQjTRpVG1KLtCNe0W5QgFW0ll4RKSRRAC5UuKReKDdHN0Tffvut1TM3K98HllQ0tmWRU1LTOLHJktcHHGLRptiE_Gj4bAs0h0eZPollDj5qYue5dh1_n_0Vf3Nl4Gw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2736325929</pqid></control><display><type>article</type><title>An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients</title><source>Springer Link</source><creator>Azamov, A. A. ; Begaliev, A. O.</creator><creatorcontrib>Azamov, A. A. ; Begaliev, A. O.</creatorcontrib><description>Pfaff equations with continuous coefficients are considered. A specific Cauchy problem for a Pfaff equation is transformed to an equivalent system of integral equations of a special type, which is overdetermined. It is shown that in the case of smooth coefficients the consistency of the system is equivalent to the Frobenius integrability criterion. A theorem on the existence of a solution for the obtained type of integral equations is presented. The solution is found by the Euler polygonal method, which allows one to construct an approximate solution of the Pfaff equation. An analog of Nagumo’s theorem on the uniqueness of the solution to the Cauchy problem is also given.</description><identifier>ISSN: 0081-5438</identifier><identifier>EISSN: 1531-8605</identifier><identifier>DOI: 10.1134/S0081543822030026</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Cauchy problems ; Coefficients ; Equivalence ; Existence theorems ; Integral equations ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Pfaff equation ; Uniqueness theorems</subject><ispartof>Proceedings of the Steklov Institute of Mathematics, 2022-08, Vol.317 (Suppl 1), p.S16-S26</ispartof><rights>Pleiades Publishing, Ltd. 2022</rights><rights>Pleiades Publishing, Ltd. 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-4fd1aaf41b907aaa0bf813efa7f595cd14e2db706a2c64612661a00c08e7245a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,27924,27925</link.rule.ids></links><search><creatorcontrib>Azamov, A. A.</creatorcontrib><creatorcontrib>Begaliev, A. O.</creatorcontrib><title>An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients</title><title>Proceedings of the Steklov Institute of Mathematics</title><addtitle>Proc. Steklov Inst. Math</addtitle><description>Pfaff equations with continuous coefficients are considered. A specific Cauchy problem for a Pfaff equation is transformed to an equivalent system of integral equations of a special type, which is overdetermined. It is shown that in the case of smooth coefficients the consistency of the system is equivalent to the Frobenius integrability criterion. A theorem on the existence of a solution for the obtained type of integral equations is presented. The solution is found by the Euler polygonal method, which allows one to construct an approximate solution of the Pfaff equation. An analog of Nagumo’s theorem on the uniqueness of the solution to the Cauchy problem is also given.</description><subject>Cauchy problems</subject><subject>Coefficients</subject><subject>Equivalence</subject><subject>Existence theorems</subject><subject>Integral equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Pfaff equation</subject><subject>Uniqueness theorems</subject><issn>0081-5438</issn><issn>1531-8605</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1UEtLAzEQDqJgrf4AbwHPq5Pn7h5LqQ-oKLSel3Q3sSlt0iZZrP_e1AoexMMwA99jZj6ErgncEsL43QygIoKzilJgAFSeoAERjBSVBHGKBge4OODn6CLGFQAXJa8HyI4cnuxtTNq1Gs-X2ge9wcp1ufBouw1-bzcqaTzz6z5Z7_CzTkvfYeMDVvjVKGPwZNerb-zDpiUee5es630f86iNsa3VLsVLdGbUOuqrnz5Eb_eT-fixmL48PI1H06IldZUKbjqilOFkUUOplIKFqQjTRpVG1KLtCNe0W5QgFW0ll4RKSRRAC5UuKReKDdHN0Tffvut1TM3K98HllQ0tmWRU1LTOLHJktcHHGLRptiE_Gj4bAs0h0eZPollDj5qYue5dh1_n_0Vf3Nl4Gw</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Azamov, A. A.</creator><creator>Begaliev, A. O.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220801</creationdate><title>An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients</title><author>Azamov, A. A. ; Begaliev, A. O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-4fd1aaf41b907aaa0bf813efa7f595cd14e2db706a2c64612661a00c08e7245a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Cauchy problems</topic><topic>Coefficients</topic><topic>Equivalence</topic><topic>Existence theorems</topic><topic>Integral equations</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Pfaff equation</topic><topic>Uniqueness theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Azamov, A. A.</creatorcontrib><creatorcontrib>Begaliev, A. O.</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the Steklov Institute of Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Azamov, A. A.</au><au>Begaliev, A. O.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients</atitle><jtitle>Proceedings of the Steklov Institute of Mathematics</jtitle><stitle>Proc. Steklov Inst. Math</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>317</volume><issue>Suppl 1</issue><spage>S16</spage><epage>S26</epage><pages>S16-S26</pages><issn>0081-5438</issn><eissn>1531-8605</eissn><abstract>Pfaff equations with continuous coefficients are considered. A specific Cauchy problem for a Pfaff equation is transformed to an equivalent system of integral equations of a special type, which is overdetermined. It is shown that in the case of smooth coefficients the consistency of the system is equivalent to the Frobenius integrability criterion. A theorem on the existence of a solution for the obtained type of integral equations is presented. The solution is found by the Euler polygonal method, which allows one to construct an approximate solution of the Pfaff equation. An analog of Nagumo’s theorem on the uniqueness of the solution to the Cauchy problem is also given.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0081543822030026</doi></addata></record>
fulltext fulltext
identifier ISSN: 0081-5438
ispartof Proceedings of the Steklov Institute of Mathematics, 2022-08, Vol.317 (Suppl 1), p.S16-S26
issn 0081-5438
1531-8605
language eng
recordid cdi_proquest_journals_2736325929
source Springer Link
subjects Cauchy problems
Coefficients
Equivalence
Existence theorems
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Pfaff equation
Uniqueness theorems
title An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T12%3A19%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20Existence%20Theorem%20and%20an%20Approximate%20Solution%20Method%20for%20a%20Pfaff%20Equation%20with%20Continuous%20Coefficients&rft.jtitle=Proceedings%20of%20the%20Steklov%20Institute%20of%20Mathematics&rft.au=Azamov,%20A.%20A.&rft.date=2022-08-01&rft.volume=317&rft.issue=Suppl%201&rft.spage=S16&rft.epage=S26&rft.pages=S16-S26&rft.issn=0081-5438&rft.eissn=1531-8605&rft_id=info:doi/10.1134/S0081543822030026&rft_dat=%3Cproquest_cross%3E2736325929%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c198t-4fd1aaf41b907aaa0bf813efa7f595cd14e2db706a2c64612661a00c08e7245a3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2736325929&rft_id=info:pmid/&rfr_iscdi=true