Skip to main content

Research Repository

Advanced Search

Heat Flow in Polygons with Reflecting Edges

Farrington, Sam; Gittins, Katie

Heat Flow in Polygons with Reflecting Edges Thumbnail


Authors

Profile image of Sam Farrington

Sam Farrington sam.farrington@durham.ac.uk
PGR Student Doctor of Philosophy



Abstract

We investigate the heat flow in an open, bounded set D in R2 with polygonal boundary ∂D. We suppose that D contains an open, bounded set D~ with polygonal boundary ∂D~. The initial condition is the indicator function of D~ and we impose a Neumann boundary condition on the edges of ∂D. We obtain an asymptotic formula for the heat content of D~ in D as time t↓0.

Citation

Farrington, S., & Gittins, K. (2023). Heat Flow in Polygons with Reflecting Edges. Integral Equations and Operator Theory, 95(4), Article 27. https://doi.org/10.1007/s00020-023-02749-0

Journal Article Type Article
Acceptance Date Oct 14, 2023
Online Publication Date Nov 7, 2023
Publication Date 2023
Deposit Date Oct 23, 2023
Publicly Available Date Nov 7, 2023
Journal Integral Equations and Operator Theory
Print ISSN 0378-620X
Electronic ISSN 1420-8989
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 95
Issue 4
Article Number 27
DOI https://doi.org/10.1007/s00020-023-02749-0
Keywords 35K20, Heat content, Reflecting edges, Polygon, 35K05
Public URL https://durham-repository.worktribe.com/output/1814450
Publisher URL https://www.springer.com/journal/20

Files

Published Journal Article (776 Kb)
PDF

Licence
http://creativecommons.org/licenses/by/4.0/

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.






You might also like



Downloadable Citations