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Title: Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient, I: Equivalence and Invertibility
Authors: Chkadua, O
Mikhailov, SE
Natroshvili, D
Keywords: Partial differential equation;Variable coefficients;Mixed problem;Boundary-domain integral equations;Pseudo-differential equations;Parametrix;Uniqueness;Invertibility
Issue Date: 2009
Publisher: Rocky Mountain Mathematics Consortium
Citation: Journal of Integral Equations and Applications 21(4): 499 - 543, Winter 2009
Abstract: 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 nonstandard 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-differential operators defined on oopen submanifolds of the boundary. It is shown that the BDIS systems are equivalent to the original mixed BVP, and the operators of the BDIE systems are invertible in appropriate Sobolev spaces.
Description: Copyright @ 2009 Rocky Mountain Mathematics Consortium
ISSN: 0897-3962
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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