Department of Quantitative Methods
Universidad Loyola Andalucía
Sevilla, 41704, Spain
email: cfresneda@uloyola.es
Department of Mathematics
Madda Walabu University
Bale Robe, P.O. Box 247, Ethiopia
email: zenebe.wogderesegn@aau.edu.et
Carlos Fresneda-Portillo, Zenebe W. Woldemicheal
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.
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.
DOI: https://doi.org/10.58997/ejde.2022.26
Show me the PDF file (375 KB), TEX file for this article.
|
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 |
Return to the EJDE web page