Brügger, Rahel and Harbrecht, Helmut and Tausch, Johannes. (2020) Boundary integral operators for the heat equation in timedependent domains. Preprints Fachbereich Mathematik, 2020 (02).

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Abstract
This article provides a functional analytical framework for boundary integral equations of the heat equation in timedependent domains. More specifically, we consider a noncylindrical domain in spacetime 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 noncylindrical domain, we introduce Sobolev spaces, trace lemmata and provide the mapping properties of the layer operators by mimicking the proofs of [M. Costabel, Boundary integral operators for the heat equation, Integral Equations and Operator Theory, 13(4):498552, 1990]. 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) 12 Special Collections > Preprints Fachbereich Mathematik 

UniBasel Contributors:  Harbrecht, Helmut and Brügger, Rahel 
Item Type:  Preprint 
Publisher:  Universität Basel 
Language:  English 
edoc DOI:  
Last Modified:  03 Nov 2020 19:10 
Deposited On:  03 Nov 2020 19:10 
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