Title On the existence and uniqueness of solution of boundary-domain integral equations for the Dirichlet problem for the nonhomogeneous heat transfer equation defined on a 2D unbounded domain
Authors Woldemicheal, Z. W., FRESNEDA PORTILLO, CARLOS, FRESNEDA PORTILLO, CARLOS
External publication No
Means Math. Meth. Appl. Sci.
Scope Article
Nature Científica
Area International
Publication date
ISI 000577531200001
DOI 10.1002/mma.6967
Abstract A system of boundary-domain integral equations (BDIEs) is obtained from the Dirichlet problem for the diffusion equation in nonhomogeneous media defined on an exterior two-dimensional domain. We use a parametrix different from the one employed in Dufera and Mikhailov (2019). The system of BDIEs is formulated in terms of parametrix-based surface and volume potentials whose mapping properties are analyzed in weighted Sobolev spaces. The system of BDIEs is shown to be equivalent to the original boundary value problem and uniquely solvable in appropriate weighted Sobolev spaces suitable for unbounded domains.
Keywords boundary-domain integral equations; Dirichlet problem; exterior problem; parametrix; remainder; unbounded domain; variable coefficient; weighted Sobolev spaces
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