University of Birmingham > Talks@bham > Analysis Seminar 2023/24 > The Heat content of polygonal domains

The Heat content of polygonal domains

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  • UserKatie Gittins (Durham University)
  • ClockMonday 02 October 2023, 15:00-16:00
  • HouseWatson LTC.

If you have a question about this talk, please contact Michael Dymond.

This talk has been canceled/deleted

Let D be a bounded subset of the plane with polygonal boundary. We impose an initial temperature condition on the complement of the boundary of D and can also impose boundary conditions on the edges of the boundary of D, such as a Dirichlet (cooling) boundary condition. In such a setting, it is natural to ask: how much heat is left inside D at time t? This quantity is the heat content of D. The small-time asymptotic expansions for the heat content of D encode information about the geometry of D and its boundary. Our goal is to explore how these expansions depend upon the geometry and on various combinations of initial and boundary conditions. We first review some of the previously known results for the small-time asymptotic expansions for the heat content of D with certain initial and boundary conditions. We then present recent results for the case where D is contained in a larger set with polygonal boundary on which a Neumann (insulating) boundary condition is imposed. The latter is based on joint work with Sam Farrington. Time-permitting, we may also discuss some geometric applications of these asymptotic expansions.

This talk is part of the Analysis Seminar 2023/24 series.

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