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A New Family of Boundary-Domain Integral Equations for the Mixed Exterior Stationary Heat Transfer Problem with Variable Coefficient

In: Integral Methods in Science and Engineering, Volume 1

Author

Listed:
  • S. E. Mikhailov

    (Brunel University West London)

  • C. F. Portillo

    (Oxford Brookes University)

Abstract

A mixed boundary value problem for the stationary heat transfer partial differential equation with variable coefficient in an exterior domain is reduced to some systems of direct segregated parametrix-based boundary-domain integral equations. We use a parametrix different from the one employed in some previous papers. Mapping properties of the potential type integral operators appearing in these equations are presented in appropriate Sobolev spaces. We prove the equivalence between the original BVP and the corresponding BDIE systems. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

Suggested Citation

  • S. E. Mikhailov & C. F. Portillo, 2017. "A New Family of Boundary-Domain Integral Equations for the Mixed Exterior Stationary Heat Transfer Problem with Variable Coefficient," Springer Books, in: Christian Constanda & Matteo Dalla Riva & Pier Domenico Lamberti & Paolo Musolino (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 0, pages 215-226, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-59384-5_19
    DOI: 10.1007/978-3-319-59384-5_19
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