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Heat Flow in Polygons with Reflecting Edges

Farrington, Sam; Gittins, Katie

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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
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

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