Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt
نویسندگان
چکیده
The boundary value problem z ′′ ρ·g·z − p /γ 1 z′ 2 3/2 − 1/r · 1 z′ 2 ·z′, r ∈ r1, r0 , z′ r1 − tan π/2 − αg , z′ r0 − tanαc, z r0 0, and z r is strictly decreasing on r1, r0 , is considered. Here, 0 < r1 < r0, ρ, g, γ, p, αc, αg are constants having the following properties: ρ, g, γ are strictly positive and 0 < π/2 − αg < αc < π/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 filmfed growth EFG method. With this aim, this study was undertaken.
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