Quarterly of Applied Mathematics
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.
Fehribach, J. D. (1993). Analysis and Application of a Continuation Method for a Self-Similar Coupled Stefan System. Quarterly of Applied Mathematics, 51(3), 405-423. Retrieved from https://digitalcommons.wpi.edu/mathematicalsciences-pubs/7
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First published in Quarterly of Applied Mathematics in 51(3), published by the American Mathematical Society.