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|Title: ||Analysis of extended boundary-domain integral and integro-differential equations of some variable-coefficient BVP|
|Authors: ||Mikhailov, SE|
|Keywords: ||partial differential equation; variable coefficients; Sobolev space; external and internal co-normal derivatives; parametrix; integral equations; integro-differential equations; equivalence; invertibility|
|Publication Date: ||2005|
|Publisher: ||University of Liverpool|
|Citation: ||In: Chen, K (ed). Advances in boundary integral methods - proceedings of the 5th UK conference on boundary integral methods. University of Liverpool, 2005|
|Abstract: ||For a function from the Sobolev space H1(Ω) definitions of non-unique external
and unique internal co-normal derivatives are considered, which are related to possible extensions of a partial differential operator and its right hand side from the domain Ω, where they are prescribed, to the domain boundary, where they are not.
The notions are then applied to formulation and analysis of direct boundary-domain integral
and integro-differential equations (BDIEs and BDIDEs) based on a specially constructed
parametrix and associated with the Dirichlet boundary value problems for the "Laplace"
linear differential equation with a variable coefficient and a rather general right hand side.
The BDI(D)Es contain potential-type integral operators defined on the domain under consideration and acting on the unknown solution, as well as integral operators defined on the boundary and acting on the trace and/or co-normal derivative of the unknown solution or on an auxiliary function. Solvability, solution uniqueness, and equivalence of the BDIEs/BDIDEs/BDIDPs to the original BVP are investigated in appropriate Sobolev spaces.|
|ISBN: ||0 906370 39 6|
|Appears in Collections:||School of Information Systems, Computing and Mathematics Research Papers|
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