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http://bura.brunel.ac.uk/handle/2438/12913
Title: | Localized boundary-domain singular integral equations of Dirichlet problem for self-adjoint second order strongly elliptic PDE systems |
Authors: | Chkadua, O Mikhailov, SE Natroshvili, D |
Keywords: | Partial differential equations;Elliptic systems;Variable coe cients;Boundary value problems;Localized parametrix;Localized boundary-domain integral equations;Pseudodifferential operators |
Issue Date: | 2016 |
Publisher: | John Wiley and Sons |
Citation: | Mathematical Methods in the Applied Sciences, (2016) |
Abstract: | The paper deals with the three dimensional Dirichlet boundary value problem (BVP) for a second order strongly elliptic self-adjoint system of partial di erential equations in the divergence form with variable coe cients and develops the integral potential method based on a localized parametrix. Using Green's representation formula and properties of the localized layer and volume potentials, we reduce the Dirichlet BVP to a system of localized boundary-domain integral equations (LBDIEs). The equivalence between the Dirichlet BVP and the corresponding LBDIE system is studied. We establish that the obtained localized boundary-domain integral operator belongs to the Boutet de Monvel algebra. With the help of the Wiener-Hopf factorization method we investigate corresponding Fredholm properties and prove invertibility of the localized operator in appropriate Sobolev (Bessel potential) spaces. |
URI: | http://onlinelibrary.wiley.com/doi/10.1002/mma.4100/abstract http://bura.brunel.ac.uk/handle/2438/12913 |
DOI: | http://dx.doi.org/10.1002/mma.4100 |
ISSN: | 1099-1476 |
Appears in Collections: | Dept of Mathematics Research Papers |
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