Fresneda-Portillo, CarlosWoldemicheal, Zenebe W.2023-04-172023-04-172022-03-04Fresneda-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. 1-15.1072-6691https://hdl.handle.net/10877/16585We 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalNon-smooth coefficientsParametrixLipschitz domainDiffusion equationBoundary-domain integral equationsMinimal wave speedArticle