Open Access
2000 Gradual loss of positivity and hidden invariant cones in a scalar heat equation
Patrick Guidotti, Sandro Merino
Differential Integral Equations 13(10-12): 1551-1568 (2000). DOI: 10.57262/die/1356061139


Invariance properties of a scalar, linear heat equation with nonlocal boundary conditions are discussed as a function of a real parameter appearing in the boundary conditions of the problem. The equation is a model for a thermostat with sensor and controller positioned at opposite ends of an interval, whence the non-locality. It is shown that the analytic semigroup associated with the evolution problem is positive if and only if the parameter is in $(-\infty,0]\,$. For the corresponding elliptic problem three maximum principles are proved which hold for different parameter ranges.


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Patrick Guidotti. Sandro Merino. "Gradual loss of positivity and hidden invariant cones in a scalar heat equation." Differential Integral Equations 13 (10-12) 1551 - 1568, 2000.


Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0983.35013
MathSciNet: MR1787081
Digital Object Identifier: 10.57262/die/1356061139

Primary: 35K20
Secondary: 35B10 , 35B32 , 35B50 , 35J25 , 47D06

Rights: Copyright © 2000 Khayyam Publishing, Inc.

Vol.13 • No. 10-12 • 2000
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