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A new family of boundary-domain integral equations for the diffusion equation with variable coefficient in unbounded domains. (English) Zbl 1460.35105

Summary: A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. This paper extends the work introduced in [C. Fresneda-Portillo, Complex Var. Elliptic Equ. 65, No. 4, 558–572 (2020; Zbl 1436.35122)] to unbounded domains. Mapping properties of parametrix-based potentials on weighted Sobolev spaces are analysed. Equivalence between the original boundary value problem and the system of BDIEs is shown. Uniqueness of solution of the BDIEs is proved using Fredholm Alternative and compactness arguments adapted to weigthed Sobolev spaces.

MSC:

35J25 Boundary value problems for second-order elliptic equations
45F15 Systems of singular linear integral equations
45P05 Integral operators

Citations:

Zbl 1436.35122
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Full Text: DOI arXiv

References:

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