Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 26, pp. 1-15.

Title: Boundary-domain integral equations for Dirichlet diffusion problems with 
       non-smooth coefficient
       
Authors: Carlos Fresneda-Portillo (Univ. Loyola Andalucia, Sevilla, Spain)
         Zenebe W. Woldemicheal (Madda Walabu Univ., Bale Robe, Ethiopia)

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
H<sup>s-2</sup>(&Omega;), 1/2&lt; s &lt;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 04, 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.