Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Mel | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 310924 13 pages doi 2008 310924 Research Article Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt Stefan Balint1 and Agneta Maria Balint2 1 Department of Computer Science Faculty of Mathematics and Computer Science West University of Timisoara 4 Vasile Parvan Boulevard 300223 Timisoara Romania 2 Faculty of Physics West University of Timisoara 4 Vasile Parvan Boulevard 300223 Timisoara Romania Correspondence should be addressed to Agneta Maria Balint balint@ Received 6 May 2008 Revised 9 June 2008 Accepted 16 October 2008 Recommended by Michel Chipot The boundary value problem z fp-g-z - p y 1 z1 2 3 - 1 r - 1 z 2 -z r e r1 r0 z r1 - tan n 2 - ag z r0 - tan ac z r0 0 and z r is strictly decreasing on r1 r0 is considered. Here 0 r1 r0 p g Y p ac ag are constants having the following properties p g Y are strictly positive and 0 n 2 - ag ac n 2. Necessary or sufficient conditions are given in terms of p 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. Copyright 2008 S. Balint and A. M. Balint. 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. 1. Introduction The free surface of the static meniscus in single crystal rod growth by EFG method in hydrostatic approximation is described by the Laplace capillary equation 1 2 1 1 . . Y R rJ p. Here Y is the melt surface tension p is the melt density g is the gravity acceleration R1 R2 are the main radii
