On United Boundary-Domain Integro-Differential Equations for Variable Coefficient Dirichlet Problem with General Right-Hand Side

Sergey E. Mikhailov () and Zenebe W. Woldemicheal ()
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Sergey E. Mikhailov: Brunel University London
Zenebe W. Woldemicheal: Addis Ababa University

Chapter Chapter 18 in Integral Methods in Science and Engineering, 2019, pp 225-235 from Springer

Abstract: Abstract The Dirichlet boundary value problem (BVP) for the linear stationary diffusion partial differential equation with a variable coefficient is considered. The PDE right-hand side belongs to the Sobolev spaces H −1(Ω), when neither classical nor canonical co-normal derivatives are well defined. Using an appropriate parametrix (Levi function) the problem is reduced to a direct boundary-domain integro-differential equation (BDIDE) or to a domain integral equation supplemented by the original boundary condition thus constituting a boundary-domain integro-differential problem (BDIDP). Solvability, solution uniqueness, and equivalence of the BDIDE/BDIDP to the original BVP are analysed in Sobolev (Bessel potential) spaces.

Date: 2019
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DOI: 10.1007/978-3-030-16077-7_18

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