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Analysis of segregated boundary‐domain integral equations for variable‐coefficient problems with cracks
Author(s) -
Chkadua O.,
Mikhailov S.E.,
Natroshvili D.
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20639
Subject(s) - mathematics , sobolev space , mathematical analysis , boundary value problem , equivalence (formal languages) , dirichlet distribution , neumann boundary condition , variable (mathematics) , partial differential equation , variable coefficient , domain (mathematical analysis) , dirichlet problem , laplace's equation , mixed boundary condition , laplace transform , dirichlet boundary condition , pure mathematics
Segregated direct boundary‐domain integral equation (BDIE) systems associated with mixed, Dirichlet and Neumann boundary value problems (BVPs) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed for domains with interior cuts (cracks). The main results established in the paper are the BDIE equivalence to the original BVPs and invertibility of the BDIE operators in the corresponding Sobolev spaces. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010