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.
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References
Chkadua, O., Mikhailov, S.E., Natroshvili, D.: Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient, I: Equivalence and invertibility. J. Integr. Equ. Appl. 21, 499–543 (2009)
Chkadua, O., Mikhailov, S.E., Natroshvili, D.: Analysis of direct segregated boundary-domain integral equations for variable-coefficient mixed BVPs in exterior domains. Anal. Appl. 11(4), 1350006 (2013)
Costabel, M.: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19, 613–626 (1988)
Giroire, J., Nedelec, J.: Numerical solution of an exterior Neumann problem using a double layer potential. Math. Comput. 32, 973–990 (1978)
Hanouzet, B.: Espaces de Sobolev avec Poids. Application au Probleme de Dirichlet Dans un Demi Espace. Rendiconti del Seminario Matematico della Universita di Padova 46, 227–272 (1971)
McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000)
Mikhailov, S.E.: Localized boundary-domain integral formulations for problems with variable coefficients. Eng. Anal. Bound. Elem. 26, 681–690 (2002)
Mikhailov, S.E.: Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains. J. Math. Anal. Appl. 378, 324–342 (2011)
Mikhailov, S.E., Portillo, C.F.: BDIE system to the mixed BVP for the Stokes equations with variable viscosity. In: Constanda, C., Kirsh, A. (eds.) Integral Methods in Science and Engineering: Theoretical and Computational Advances. Springer (Birkhäuser), Boston (2015)
Mikhailov, S.E., Portillo, C.F.: A new family of boundary-domain integral equations for a mixed elliptic BVP with variable coefficient. In: Proceedings of the 10th UK Conference on Boundary Integral Methods. Brighton University Press, Brighton (2015)
Miranda, C.: Partial Differential Equations of Elliptic Type, 2nd edn. Springer, Berlin (1970)
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Mikhailov, S.E., Portillo, C.F. (2017). A New Family of Boundary-Domain Integral Equations for the Mixed Exterior Stationary Heat Transfer Problem with Variable Coefficient. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_19
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DOI: https://doi.org/10.1007/978-3-319-59384-5_19
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