Boundary-domain integral equations for Dirichlet diffusion problems with non-smooth coefficient

Date

2022-03-04

Authors

Fresneda-Portillo, Carlos
Woldemicheal, Zenebe W.

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We obtain a system of boundary-domain integral equations (BDIE) equivalent to the Dirichlet problem for the diffusion equation in non-homogeneous media. We use an extended version of the boundary integral method for PDEs with variable coefficients for which a parametrix is required. We generalize existing results for this family of parametrices considering a non-smooth variable coefficient in the PDE and source term in Hs-2(Ω), 1/2 < s < 3/2 defined on a Lipschitz domain. The main results concern the equivalence between the original BVP and the corresponding BDIE system, as well as the well-posedness of the BDIE system.

Description

Keywords

Non-smooth coefficients, Parametrix, Lipschitz domain, Diffusion equation, Boundary-domain integral equations, Minimal wave speed

Citation

Fresneda-Portillo, C., & Woldemicheal, Z. W. (2022). Boundary-domain integral equations for Dirichlet diffusion problems with non-smooth coefficient. <i>Electronic Journal of Differential Equations, 2022</i>(26), pp. 1-15.

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Attribution 4.0 International

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