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
Journal ISSN
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. Electronic Journal of Differential Equations, 2022(26), pp. 1-15.
Rights
Attribution 4.0 International