The thermostat problem with a nonlocal nonlinear boundary condition

G. Kalna, S. McKee

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13 Citations (Scopus)


The thermostat controller for an air-conditioning system is usually placed in a position at some distance from the unit and this can lead to large swings in temperature. This paper addresses this question by studying a paradigm - a one-dimensional heat conduction equation with and without heat loss, and where the flux of heat extracted or input by the unit is considered to be a function of the temperature at the other end. The essential results are that the system can be unstable and that this is exacerbated both by a more powerful air-conditioning unit and by more efficient insulation.
Original languageEnglish
Pages (from-to)437-462
Number of pages25
JournalIMA Journal of Applied Mathematics
Issue number5
Publication statusPublished - 2004


  • heat equation
  • nonlocal boundary condition
  • Volterra integral equation

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