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Boundary integral operators for the heat equation

Brügger, Rahel and Harbrecht, Helmut and Tausch, Johannes. (2022) Boundary integral operators for the heat equation. Integral Equations and Operator Theory, 94 (2). p. 10.

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Official URL: https://edoc.unibas.ch/88061/

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Abstract

This article provides a functional analytical framework for boundary integral equations of the heat equation in time-dependent domains. More specifically, we consider a non-cylindrical domain in space-time that is the C 2 -diffeomorphic image of a cylinder, i.e., the tensor product of a time interval and a fixed domain in space. On the non-cylindrical domain, we introduce Sobolev spaces, trace lemmata and provide the mapping properties of the layer operators. Here it is critical that the Neumann trace requires a correction term for the normal velocity of the moving boundary. Therefore, one has to analyze the situation carefully.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Brügger, Rahel Christina
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:0378-620X
e-ISSN:1420-8989
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
edoc DOI:
Last Modified:29 Mar 2022 12:25
Deposited On:29 Mar 2022 12:25

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