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Spring 2020 Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain
S. E. Mikhailov, C. F. Portillo
J. Integral Equations Applications 32(1): 59-75 (Spring 2020). DOI: 10.1216/JIE.2020.32.59

Abstract

A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed in previous papers by Mikhailov (2002, 2006) and Chkadua, Mikhailov and Natroshvili (2009). We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

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S. E. Mikhailov. C. F. Portillo. "Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain." J. Integral Equations Applications 32 (1) 59 - 75, Spring 2020. https://doi.org/10.1216/JIE.2020.32.59

Information

Received: 31 March 2017; Revised: 19 September 2018; Accepted: 25 September 2018; Published: Spring 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07223723
MathSciNet: MR4115972
Digital Object Identifier: 10.1216/JIE.2020.32.59

Subjects:
Primary: 31B10 , 35J25 , 45A05 , 45K05

Keywords: boundary-domain integral equations , Mixed boundary value problem , Parametrix , remainder , variable coefficient

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 1 • Spring 2020
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