Nonlinear boundary value problem for concave capillary surfaces occurring in single crystal rod growth from the melt
by
Stefan Balint
West University of Timisoara Department of Computer Science
Coauthors: Agneta M.Balint (West University of Timisoara)

In this paper the boundary value problem:

ì ï ï ï í ï ï ï î z"= r·g·z-p g [1+(z')2 ][3/2] - 1 r ·[1+(z')2 ]·z       r ∈ [r1,   R0 ] z'(r1)=-tan æ è p 2 -ag ö ø z'(R0)=-tan ac z(R0 )=0  and    z(r)    is  strictly  decreasing  on  [r1 ,  R0]

(1)

is considered.

Here: 0 < r₁ < R₀ ,     r,   g,   g,   p,   a_c ,   a_g are constants having the following properties:   r,   g,   g are strictly positive and 0 < [(p)/2] -a_g < a_c < [(p)/2].

Necessary and sufficient conditions are given in terms of p for the existence of concave solutions of the problem (1). This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt. Numerical example is given.

Date received: March 6, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caub-71.