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Analysis of Segregated Boundary–Domain Integral Equations for Mixed Variable-Coefficient BVPs in Exterior Domains

In: Integral Methods in Science and Engineering

Author

Listed:
  • O. Chkadua

    (A.Razmadze Mathematical Institute)

  • S. E. Mikhailov

    (Brunel University West London)

  • D. Natroshvili

    (Georgian Technical University)

Abstract

Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.

Suggested Citation

  • O. Chkadua & S. E. Mikhailov & D. Natroshvili, 2011. "Analysis of Segregated Boundary–Domain Integral Equations for Mixed Variable-Coefficient BVPs in Exterior Domains," Springer Books, in: Christian Constanda & Paul J. Harris (ed.), Integral Methods in Science and Engineering, edition 1, pages 109-128, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8238-5_11
    DOI: 10.1007/978-0-8176-8238-5_11
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