Electron. J. Differential Equations, Vol. 2022 (2022), No. 26, pp. 1-15.

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

Carlos Fresneda-Portillo, Zenebe W. Woldemicheal

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.

Submitted May 31, 2021. Published March 4, 2022.
Math Subject Classifications: 35J25, 31B10, 45K05, 45A05.
Key Words: Non-smooth coefficients; parametrix; Lipschitz domain; diffusion equation; boundary-domain integral equations; minimal wave speed.

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Carlos Fresneda Portillo
Department of Quantitative Methods
Universidad Loyola Andalucía
Sevilla, 41704, Spain
email: cfresneda@uloyola.es
Zenebe W. Woldemicheal
Department of Mathematics
Madda Walabu University
Bale Robe, P.O. Box 247, Ethiopia
email: zenebe.wogderesegn@aau.edu.et

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