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Properties of some ordinary differential equations related to free boundary problems

Published online by Cambridge University Press:  14 November 2011

Gunduz Caginalp  and
Stuart Hastings
Gunduz Caginalp
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
Stuart Hastings
Affiliation:
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14214-3093, U.S.A.
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Synopsis

Some second order ordinary differential equations of the form ξ2ϕ″ + ξ2(N − 1)″′/r + ½(ϕ − ϕ3) + ½k = 0 are studied. Properties such as existence and monotonicity of solutions are considered for N ≧ 1, ξ > 0 and two sets of boundary conditions. For N = 1, some explicit results are obtained for small ξ. These ODE's arise from a phase field approach to free boundary problems involving a phase transition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 104 , Issue 3-4 , 1986 , pp. 217 - 234
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

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