ANALYSIS OF DIRECT BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR A MIXED BVP WITH VARIABLE COEFFICIENT, I: EQUIVALENCE AND INVERTIBILITY
A mixed (Dirichlet-Neumann) boundary value problem (BVP) for the "stationary heat transfer" partial differential equation with variable coefficient is reduced to some systems of nonstandard segregated direct parametrix-based boundary-domain integral equations (BDIEs). The BDIE systems cont...
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| Veröffentlicht in: | The Journal of integral equations and applications 2009-12, Vol.21 (4), p.499-543 |
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| container_title | The Journal of integral equations and applications |
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| creator | CHKADUA, O. MIKHAILOV, S.E. NATROSHVILI, D. |
| description | A mixed (Dirichlet-Neumann) boundary value problem (BVP) for the "stationary heat transfer" partial differential equation with variable coefficient is reduced to some systems of nonstandard segregated direct parametrix-based boundary-domain integral equations (BDIEs). The BDIE systems contain integral operators defined on the domain under consideration as well as potential-type and pseudodifferential operators defined on open submanifolds of the boundary. It is shown that the BDIE systems are equivalent to the original mixed BVP, and the operators of the BDIE systems are invertible in appropriate Sobolev spaces. |
| doi_str_mv | 10.1216/JIE-2009-21-4-499 |
| format | Article |
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The BDIE systems contain integral operators defined on the domain under consideration as well as potential-type and pseudodifferential operators defined on open submanifolds of the boundary. It is shown that the BDIE systems are equivalent to the original mixed BVP, and the operators of the BDIE systems are invertible in appropriate Sobolev spaces.</description><subject>Boundary value problems</subject><subject>boundary-domain integral equations</subject><subject>Cardiac resynchronization therapy</subject><subject>Differential equations</subject><subject>existence</subject><subject>Invertibility</subject><subject>Mathematical functions</subject><subject>Mathematical integrals</subject><subject>Mathematics</subject><subject>mixed problem</subject><subject>parametrix</subject><subject>Partial differential equation</subject><subject>Partial differential equations</subject><subject>pseudo-differential equations</subject><subject>Uniqueness</subject><subject>Variable coefficients</subject><issn>0897-3962</issn><issn>1938-2626</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNo9kUFPgzAYhhujiXP6AzyY9AdYbQsU6q2Dsn2GgTI23anpgCVbNCwwDx7957Js2elLvuR5Du-D0D2jT4wz8fwKmnBKJeGMuMSV8gINmHQCwgUXl2hAA-kTRwp-jW66bkspcz0pBuhPpSpZzmCGsxhHkOuwwKNsnkYqX5IomypIMaSFHucqwfp9rgrI0hmOsxwrPIVPHeHR4g1_QDHBC5WDGiUah5mOYwhBp8UjhpcDBwuV6DTUWKVRL1zovIARJFAsb9HV2n519d3pDtE81kU4IUk2hlAlpHREsCfcCt8VtZV-vXKkG0jP5UFty7VHbeVX3ppVPKh86TBrPetWXFLfZysqPGlXXFpniNTRu2ubbV3u65_ya1OZXbv5tu2vaezGhPPk9D2d7aa2hvUTcr_fK-gd7Ogo26br2np9xhk1hw6m72AOHQxnxjV9h555ODLbbt-0Z4ALJhwhuPMP0pV7Fw</recordid><startdate>20091201</startdate><enddate>20091201</enddate><creator>CHKADUA, O.</creator><creator>MIKHAILOV, S.E.</creator><creator>NATROSHVILI, D.</creator><general>The Rocky Mountain Mathematics Consortium</general><general>Rocky Mountain Mathematics Consortium</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20091201</creationdate><title>ANALYSIS OF DIRECT BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR A MIXED BVP WITH VARIABLE COEFFICIENT, I: EQUIVALENCE AND INVERTIBILITY</title><author>CHKADUA, O. ; MIKHAILOV, S.E. ; NATROSHVILI, D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-2a6746ea97eb394895428eacf50ad7d5f1d28d7931aa5a4d290771b0659ab29a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Boundary value problems</topic><topic>boundary-domain integral equations</topic><topic>Cardiac resynchronization therapy</topic><topic>Differential equations</topic><topic>existence</topic><topic>Invertibility</topic><topic>Mathematical functions</topic><topic>Mathematical integrals</topic><topic>Mathematics</topic><topic>mixed problem</topic><topic>parametrix</topic><topic>Partial differential equation</topic><topic>Partial differential equations</topic><topic>pseudo-differential equations</topic><topic>Uniqueness</topic><topic>Variable coefficients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>CHKADUA, O.</creatorcontrib><creatorcontrib>MIKHAILOV, S.E.</creatorcontrib><creatorcontrib>NATROSHVILI, D.</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of integral equations and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CHKADUA, O.</au><au>MIKHAILOV, S.E.</au><au>NATROSHVILI, D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ANALYSIS OF DIRECT BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR A MIXED BVP WITH VARIABLE COEFFICIENT, I: EQUIVALENCE AND INVERTIBILITY</atitle><jtitle>The Journal of integral equations and applications</jtitle><date>2009-12-01</date><risdate>2009</risdate><volume>21</volume><issue>4</issue><spage>499</spage><epage>543</epage><pages>499-543</pages><issn>0897-3962</issn><eissn>1938-2626</eissn><abstract>A mixed (Dirichlet-Neumann) boundary value problem (BVP) for the "stationary heat transfer" partial differential equation with variable coefficient is reduced to some systems of nonstandard segregated direct parametrix-based boundary-domain integral equations (BDIEs). The BDIE systems contain integral operators defined on the domain under consideration as well as potential-type and pseudodifferential operators defined on open submanifolds of the boundary. It is shown that the BDIE systems are equivalent to the original mixed BVP, and the operators of the BDIE systems are invertible in appropriate Sobolev spaces.</abstract><pub>The Rocky Mountain Mathematics Consortium</pub><doi>10.1216/JIE-2009-21-4-499</doi><tpages>45</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | The Journal of integral equations and applications, 2009-12, Vol.21 (4), p.499-543 |
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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | Boundary value problems boundary-domain integral equations Cardiac resynchronization therapy Differential equations existence Invertibility Mathematical functions Mathematical integrals Mathematics mixed problem parametrix Partial differential equation Partial differential equations pseudo-differential equations Uniqueness Variable coefficients |
| title | ANALYSIS OF DIRECT BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR A MIXED BVP WITH VARIABLE COEFFICIENT, I: EQUIVALENCE AND INVERTIBILITY |
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