Continuous dependence results for a class of nonlinear heat equations in a cylindrical region

In this paper, we derive bounds for the solutions of a quasilinear heat equation in a finite cylindrical region if the far end and the lateral surface are held at zero temperature, and a nonzero temperature is applied at the near end. Some continuous dependence inequalities are also obtained. We als...

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Veröffentlicht in:	Mathematical methods in the applied sciences 2009-02, Vol.32 (3), p.330-345
Hauptverfasser:	Philippin, G. A., Proytcheva, V., Vernier-Piro, S.
Format:	Artikel
Sprache:	eng
Schlagworte:	continuous dependence inequalities Exact sciences and technology Mathematical analysis Mathematics Partial differential equations quasilinear parabolic problems Sciences and techniques of general use
Online-Zugang:	Volltext
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Zusammenfassung:	In this paper, we derive bounds for the solutions of a quasilinear heat equation in a finite cylindrical region if the far end and the lateral surface are held at zero temperature, and a nonzero temperature is applied at the near end. Some continuous dependence inequalities are also obtained. We also investigate the case in which a given heat flux is prescribed at the near end, instead of a given temperature. Copyright © 2008 John Wiley & Sons, Ltd.
ISSN:	0170-4214 1099-1476
DOI:	10.1002/mma.1040