Title BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR DIRICHLET DIFFUSION PROBLEMS WITH NON-SMOOTH COEFFICIENT
Authors FRESNEDA PORTILLO, CARLOS, Woldemicheal, Zenebe W.
External publication No
Means Electron. J. Differ. Equ.
Scope Article
Nature Científica
JCR Quartile 2
SJR Quartile 3
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85128711621&partnerID=40&md5=3341115c6a7222a5ee6d67513892eac1
Publication date 04/03/2022
ISI 000782726300001
Scopus Id 2-s2.0-85128711621
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(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.
Keywords Non-smooth coefficients; parametrix; Lipschitz domain; diffusion equation; boundary-domain integral equations; minimal wave speed
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