FRESNEDA PORTILLO, CARLOS, Woldemicheal, Zenebe W.
No
Electron. J. Differ. Equ.
Article
Científica
0.7
0.412
31/03/2022
000782726300001
2-s2.0-85128711621
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(Omega), 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.
Non-smooth coefficients; parametrix; Lipschitz domain; diffusion equation; boundary-domain integral equations; minimal wave speed