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

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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Correspondence to Agneta Maria Balint.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Balint, S., Balint, A.M. Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt. J Inequal Appl 2008, 310924 (2008). https://doi.org/10.1155/2008/310924

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  • DOI: https://doi.org/10.1155/2008/310924

Keywords

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  • Nonlinear Boundary
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  • Capillary Surface