Analysis and application of a continuation method for a self-similar coupled Stefan system

Author:
Joseph D. Fehribach

Journal:
Quart. Appl. Math. **51** (1993), 405-423

MSC:
Primary 80A22; Secondary 35K55, 65H20

DOI:
https://doi.org/10.1090/qam/1233522

MathSciNet review:
MR1233522

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Abstract | References | Similar Articles | Additional Information

Abstract: This work deals with a continuation method for computing solutions to a self-similar two-component Stefan system in which the diffusion coefficients depend on the concentrations. The procedure computes a one-parameter homotopy connecting the known solution of a simplified problem (when the parameter is zero) to the solution of the problem at hand (when the parameter is one). Local convergence of the method and local existence and uniqueness of solutions for the original system are proven. Also, several examples coming from precipitant-driven protein crystal growth are discussed. The most interesting of these is a Stefan problem containing a porous media equation that corresponds to the liquid phase being in a meta-stable state near the spinodal region. The bifurcation code AUTO is used in the computations.

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DOI:
https://doi.org/10.1090/qam/1233522

Article copyright:
© Copyright 1993
American Mathematical Society