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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/3745

Title: About analysis of some localized boundary-domain integral equations for a variable-coefficient BVPs
Authors: Chkadua, O
Mikhailov, SE
Natroshvili, D
Keywords: partial differential equations; variable coefficients; parametrix; localisation; boundary-domain integral equation; pseudo-differential operators
Publication Date: 2007
Publisher: Durham University
Citation: In: Trevelyan, J (ed). Advances in boundary integral methods - proceedings of the sixth UK conference on boundary integral methods. Durham University, 2007
Abstract: Some direct localized boundary-domain integral equations (LBDIEs) associated with the Dirichlet and Neumann boundary value problems for the "Laplace" linear differential equation with a variable coefficient are formulated. The LBDIEs are based on a parametrix localized by a cut-off function. Applying the theory of pseudo-differential operators, invertibility of the localized volume potentials is proved first. This allows then to prove solvability, solution uniqueness and equivalence of the LBDIEs to the original BVP, and investigate the LBDIE operator invertibility in appropriate Sobolev spaces.
URI: http://bura.brunel.ac.uk/handle/2438/3745
ISBN: 978-0-9535558-3-3
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers

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