ANALYSIS OF DIRECT BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR A MIXED BVP WITH VARIABLE COEFFICIENT, I: EQUIVALENCE AND INVERTIBILITY

被引：50

作者：

Chkadua, O. ^{[1
,2
]}

Mikhailov, S. E. ^{[3
]}

Natroshvili, D. ^{[4
]}

机构：

[1] Georgian Acad Sci, A Razmadze Math Inst, GE-0193 Tbilisi, Georgia

[2] Georgia & Sukhumi Univ, GE-0186 Tbilisi, Georgia

[3] Brunel Univ, Dept Math, Uxbridge UB8 3PH, Middx, England

[4] Georgian Tech Univ, Dept Math, GE-0175 Tbilisi, Georgia

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2009年 / 21卷 / 04期

关键词：

Partial differential equation; variable coefficients; mixed problem; parametrix; boundary-domain integral equations; pseudo-differential equations; existence; uniqueness; invertibility; OPERATORS; SYSTEMS;

D O I：

10.1216/JIE-2009-21-4-499

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 nonstandared 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 pseudo-differetial opeators 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 BDIE systems are invertible in appropriate Sobolev spaces.

引用

页码：499 / 543

页数：45

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