Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Waiting time phenomena forced by critical boundary conditions in classical diffusion problems


Authors: A. Fasano, A. Mancini, M. Primicerio and B. Zaltzman
Journal: Quart. Appl. Math. 69 (2011), 105-122
MSC (2000): Primary 35K60
DOI: https://doi.org/10.1090/S0033-569X-2010-01205-0
Published electronically: December 29, 2010
MathSciNet review: 2807980
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper revisits some very classical initial-boundary value problems for parabolic equations, providing simple examples in which the occurrence of flux discontinuities at the boundary when the unknown function reaches some critical value may give rise to a waiting time phenomenon. A physical interpretation could be a modification of the surface of the considered body taking place at the mentioned critical value, affecting the way the body interacts with the surroundings. The waiting time, whose length (finite or infinite) is a priori unknown allows the system to evolve gradually through the critical state. Some numerical simulations are also presented.


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Additional Information

A. Fasano
Affiliation: Dip. di Matematica “U.Dini” - Universitá degli Studi di Firenze, viale Morgagni, 67a - 50134 Firenze, Italy
Email: fasano@math.unifi.it

A. Mancini
Affiliation: Dip. di Matematica “U.Dini” - Universitá degli Studi di Firenze, viale Morgagni, 67a - 50134 Firenze, Italy
Email: mancini@math.unifi.it

M. Primicerio
Affiliation: Dip. di Matematica “U.Dini” - Universitá degli Studi di Firenze, viale Morgagni, 67a - 50134 Firenze, Italy
Email: primicerio@math.unifi.it

B. Zaltzman
Affiliation: DSEEP, Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede-Boker Campus, 84990, Israel
Email: boris@bgumail.bgu.ac.il

DOI: https://doi.org/10.1090/S0033-569X-2010-01205-0
Received by editor(s): July 21, 2009
Published electronically: December 29, 2010
Article copyright: © Copyright 2010 Brown University


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