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Surface tension, higher order phase field equations, dimensional analysis and Clairaut’s equation
Mathematics Department University of Pittsburgh, Pittsburgh, PA 15260, USA
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Special Issue: Nonlinear Evolution PDEs, Interfaces and Applications
1. G. Barenblatt and P. Makinen, Dimensional Analysis, Routledge, Taylor and Francis, Abingdon, UK, 1987.
2. M. Ben Amar, Dendritic growth rate at arbitrary undercooling, Phys. Rev. A., 41 (1990), 2080-2092.
3. G. Caginalp, A microscopic derivation of macroscopic phase boundary problems, Journal of Statistical Physics, 59 (1990), 869-884.
4. M. Conti, Thermal and chemical diffusion in the rapid solidification of binary alloys, Phys. Rev. E., 61 (2000), 642-650.
5. G. Caginalp and E. Esenturk, Anisotropic Phase Field Equations of Arbitrary Order, Discrete and Continuous Dynamical Systems, Series S 4 (2011), 311-350.
6. G. Caginalp and E. Esenturk, Renormalization Methods for Higher Order Differential Equations, J. Physics A., 47 (2014), 315004.
7. G. Caginalp and P. Fife, Higher order phase field models and detailed anisotropy, Physical Review B., 34 (1986), 4940-4943.
8. L.C. Evans, Partial Differential Equations, American Math Soc., Providence, RI, 2010.
9. N. Goldenfeld, Lectures on phase transitions and renormalization group, Perseus Books, 1992.
10. A. Miranville, Higher-order anisotropic Caginalp phase-field systems Mediterr. J. Math., 13 (2016), 4519-4535.
11. M. Niezgodka and P. Strzelecki, Free Boundary Problems, Theory and Applications Proceedings of the Zakopane Conference, 1995.
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