Journal Article

A new family of boundary-domain integral equations for the Dirichlet Problem of the diffusion equation in nhomogeneous media with H −1 (Ω) source term on Lipschitz Domains

Abstract

The interior Dirichlet boundary value problem for the diffusion equation in nonhomogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in 1 different from2. We further extend the results obtained in 1 for the mixed problem in a smooth domain with L²(Ω) hand side to Lipschitz domains and PDE right-hand in the Sobolev space H¯(Ω), where neither the classical nor the canonical co-normal derivatives are well defined. Equivalence between the system of BDIEs and the original BVP is proved along with their solvability and solution uniqueness in appropriate Sobolev spaces.

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Authors

Fresneda-Portillo, Carlos
Woldemicheal, Zenebe W.

Oxford Brookes departments

School of Engineering, Computing and Mathematics

Dates

Year of publication: 2020
Date of RADAR deposit: 2020-06-11

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

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Related resources

This RADAR resource is Identical to A new family of boundary‐domain integral equations for the Dirichlet problem of the diffusion equation in inhomogeneous media with H −1(Ω) source term on Lipschitz domains
This RADAR resource is the Version of Record of [preprint:] A New Family of Boundary-Domain Integral Equations for the Dirichlet Problem of the Diffusion Equation in Inhomogeneous Media with H-1(Ω) Source Term on Lipschitz Domains