Open Access

Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt

Journal of Inequalities and Applications20082008:310924

DOI: 10.1155/2008/310924

Received: 6 May 2008

Accepted: 16 October 2008

Published: 20 November 2008

Abstract

The boundary value problem , , , , and is strictly decreasing on , is considered. Here, are constants having the following properties: are strictly positive and . Necessary or sufficient conditions are given in terms of for the existence of concave solutions of the above nonlinear boundary value problem (NLBVP). Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by edge-defined film-fed growth (EFG) method. With this aim, this study was undertaken.

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Authors’ Affiliations

(1)
Department of Computer Science, Faculty of Mathematics and Computer Science, West University of Timisoara
(2)
Faculty of Physics, West University of Timisoara

Copyright

© S. Balint and A. M. Balint. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.