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DC Field | Value | Language |
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dc.contributor.author | Chkadua, O | - |
dc.contributor.author | Mikhailov, SE | - |
dc.contributor.author | Natroshvili, D | - |
dc.date.accessioned | 2016-07-07T15:05:18Z | - |
dc.date.available | 2016-07-07T15:05:18Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Mathematical Methods in the Applied Sciences, (2016) | en_US |
dc.identifier.issn | 1099-1476 | - |
dc.identifier.uri | http://onlinelibrary.wiley.com/doi/10.1002/mma.4100/abstract | - |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/12913 | - |
dc.description.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. | en_US |
dc.description.sponsorship | This research was supported by the grants EP/H020497/1: "Mathematical Analysis of Localized Boundary-Domain Integral Equations for Variable-Coeff cient Boundary Value Problems" and EP/M013545/1: "Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs", from the EPSRC, UK, and by the grant of the Shota Rustaveli National Science Foundation FR/286/5-101/13, 2014- 2017: "Investigation of dynamical mathematical models of elastic multi-component structures with regard to fully coupled thermo-mechanical and electro-magnetic fields". | en_US |
dc.language.iso | en | en_US |
dc.publisher | John Wiley and Sons | en_US |
dc.subject | Partial differential equations | en_US |
dc.subject | Elliptic systems | en_US |
dc.subject | Variable coe cients | en_US |
dc.subject | Boundary value problems | en_US |
dc.subject | Localized parametrix | en_US |
dc.subject | Localized boundary-domain integral equations | en_US |
dc.subject | Pseudodifferential operators | en_US |
dc.title | Localized boundary-domain singular integral equations of Dirichlet problem for self-adjoint second order strongly elliptic PDE systems | en_US |
dc.type | Article | en_US |
dc.identifier.doi | http://dx.doi.org/10.1002/mma.4100 | - |
dc.relation.isPartOf | Mathematical Methods in the Applied Sciences | - |
pubs.publication-status | Accepted | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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