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Title: Localized direct segregated boundary-domain integral equations for variable-coefficient transmission problems with interface crack
Authors: Chkadua, O
Mikhailov, SE
Natroshvili, D
Keywords: Partial differential equation
Transmission problem
Interface crack problem
Mixed problem
Localized parametrix
Localized boundary-domain integral equation
Pseudo-differential equation
Publication Date: 2011
Publisher: Georgian National Academy of Sciences and the A. Razmadze Mathematical Institute
Citation: Memoirs on Differential Equations and Mathematical Physics, 52: 17-64, 2011
Abstract: Some transmission problems for scalar second order elliptic partial differential equations are considered in a bounded composite domain consisting of adjacent anisotropic subdomains having a common interface surface. The matrix of coefficients of the differential operator has a jump across the interface but in each of the adjacent subdomains is represented as the product of a constant matrix by a smooth variable scalar function. The Dirichlet or mixed type boundary conditions are prescribed on the exterior boundary of the composite domain, the Neumann conditions on the the interface crack surfaces and the transmission conditions on the rest of the interface. Employing the parametrix-based localized potential method, the transmission problems are reduced to the localized boundary-domain integral equations. The corresponding localized boundary-domain integral operators are investigated and their invertibility in appropriate function spaces is proved.
Description: The full text of the published article can be accessed at the link below
Sponsorship: This research was supported by EPSRC grant No. EP/H020497/1 and partly by the Georgian Technical University grant
ISSN: 1512-0015
Appears in Collections:Mathematical Science
Dept of Mathematics Research Papers

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