Stable and unstable initial configuration in the theory wave fronts

Ruediger Landes

doi:10.3934/dcdss.2012.5.797

Article Contents

2012, Volume 5, Issue 4: 797-808. Doi: 10.3934/dcdss.2012.5.797

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Stable and unstable initial configuration in the theory wave fronts

Ruediger Landes^1,

1.
University of Oklahoma, Noman, OK 73019

Received: February 28, 2011

Revised: April 30, 2011

Published: July 2012

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Abstract

In this paper we study the wavefront like phase transition of solutions of a parabolic nonlinear boundary value problem used to model phase transitions in the theory of boiling liquids. Using weak supersolutions we provide bounds for the propagation speed of such a phase transition. Also we construct stable supersolutions to initial configurations which have locally supercritical values.

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Mathematics Subject Classification: Primary: 35K99, Secondary: 35B35, 35B40, 35D30.

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References

[1]	D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math., 30 (1978), 33-76.doi: 10.1016/0001-8708(78)90130-5.
[2]	H. Auracher, W. Marquardt, M. Buchholz, R. Hohl, T. Lüttich and J. Blum, New experimental results on steady-state and transient pool boiling heat transfer, Therm. Sci. Engng, 9 (2001), 29-39.
[3]	J. Blum, T. Lüttich and W. Marquardt, Temperature Wave Propagation as a Route from Nucleate to Film Boiling?, In "2nd International Symposium on Two-Phase Flow Modelling and Experimentation" (eds. G. P. Celata, P. DiMarco and R. K. Shah), 1, Rome, Edizioni ETS, Pisa, (1999), 137-144.
[4]	V. K. Dhir, Boiling heat transfer, Annu. Rev. Fluid Mech., 30 (1998), 365-401.doi: 10.1146/annurev.fluid.30.1.365.
[5]	P. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Lecture Notes in Biomathematics, 28, Springer-Verlag, Berlin-New York, 1979.
[6]	R. Landes, Wavefront solution in the theory of boiling liquids, Analysis (Munich), 29 (2009), 283-298.
[7]	T. Lüttich, W. Marquardt, M. Buchholz and H. Auracher, "Towards a Unifying Heat Transfer Correlation for the Entire Boiling Curve," 5th International Conference on Boiling Heat Transfer, Montego Bay, Jamaica, May 2003.
[8]	M. Speetjens, A. Reusken and W. Marquardt, Steady-state solutions in a nonlinear pool boiling model, Commun. Nonlinear Sci. Numer. Simul., 13 (2008), 1475-1494.doi: 10.1016/j.cnsns.2006.11.001.
[9]	M. Speetjens, A. Reusken and W. Marquardt, Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model, Commun. Nonlinear Sci. Numer. Simul., 13 (2008), 1518-1537.doi: 10.1016/j.cnsns.2006.11.002.
[10]	J. R. Thome, Boiling, in "Handbook of Heat Transfer" (eds. A. Bejan and A. D. Krause), Wiley & Sons, New York, (2003), 635-717.