Mathematical analysis of a model describing solute trapping during solidification of binary alloys

References

• Aziz MJ, Kaplan T. Continuous growth model for interface motion during alloy solidification. Acta Metall. 1988;36:2335–2348.
   Google Scholar
• Kittl JA, Sanders PG, Aziz MJ, et al. Complete experimental test of kinetic models for rapid alloy solidification. Acta Mater. 2000;48:4797–4811.
   Web of Science ®Google Scholar
• Galenko PK, Abramova EV, Herlach DM. Phase-field study of solute trapping effect in rapid solidification. Discrete Cont Dyn Syst. 2011; Dynamical systems, differential equations and applications. 8th AIMS Conference. Suppl. Vol. I: 457–466.
   Google Scholar
• Buchbinder GL, Galenko PK. Boundary interface conditions and solute trapping near the transition to diffusionless solidification. Eur Phys J Special Topics. 2020;229:287–294.
   Web of Science ®Google Scholar
• Wheeler AA, Boettinger WJ, McFadden GB. Phase-field model of solute trapping during solidification. Phys Rev E. 1993;47:1893–1909.
   Web of Science ®Google Scholar
• Wheeler AA, Boettinger WJ, McFadden GB. Phase-field model for isothermal phase transitions in binary alloys. Phys Rev A. 1992;45:7424–7439.
   PubMed Web of Science ®Google Scholar
• Barrett JW, Blowey JF. Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility. Math Comput. 1999;68:487–517.
   Web of Science ®Google Scholar
• Schimperna G. Global attractors for Cahn-Hilliard equations with nonconstant mobility. Nonlinearity. 2007;20:2365–2387.
   Web of Science ®Google Scholar
• Schimperna G, Zelik S. Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Trans Am Math Soc. 2013;365:3799–3829.
   Web of Science ®Google Scholar
• Cahn JW, Novick-Cohen A. Evolution equations for phase separation and ordering in binary alloys. J Stat Phys. 1994;76:877–909.
   Web of Science ®Google Scholar
• Brochet D, Hilhorst D, Novick-Cohen A. Finite-Dimensional exponential attractor for a model for order-disorder and phase separation. Appl Math Lett. 1994;7:83–87.
   Web of Science ®Google Scholar
• Miranville A, Saoud W, Talhouk R. Asymptotic behavior of a model for order-disorder and phase separation. Asymptot Anal. 2017;103:57–76.
   Web of Science ®Google Scholar
• Miranville A, Saoud W, Talhouk R. On the Cahn-Hilliard/Allen-Cahn equations with singular potentials. Discrete Cont Dyn Syst Ser B. 2019;24(8):3633–3651.
   Web of Science ®Google Scholar
• Dal Passo R, Giacomelli L, Novick-Cohen A. Existence for an Allen-Cahn/Cahn-Hilliard system with degenerate mobility. Interfaces Free Bound. 1999;1:199–226.
   Google Scholar
• Elliott CM, Garcke H. On the Cahn-Hilliard equation with degenerate mobility. Siam J Math Anal. 1996;27(2):404–423.
   Web of Science ®Google Scholar
• Scheid JF. Global solutions to a degenerate solutal phase-field model for the solidification of a binary alloy. Nonlinear Anal Real World Appl. 2004;5:207–217.
   Web of Science ®Google Scholar
• Le Dret H. Nonlinear elliptic partial differential equations. Cham: Universitext, Elsevier; 2018.
   Google Scholar
• Ferreira e Pereira A, Planas G. Analysis of a three-dimensional phase-field model for solidification under a magnetic field effect. J Math Anal Appl. 2020;482(1):123494.
   Google Scholar
• Kesavan S. Topics in functional analysis and applications. New York: John Wiley & Sons; 1989.
   Google Scholar
• Folland GB. Introduction to partial differential equations. 2nd ed. Princeton: Princeton University Press; 1995.
   Google Scholar
• Simon J. Compact sets in the space Lp(0,T;B). Ann Mat Pura Appl. 1986;146(1):65–96.
   Google Scholar
• Adams RA, Fournier JJFSobolev spaces. Vancouver: Academic Press; 2005.
   Google Scholar
• Mitrinovic DS, Pecaric J, Fink AM. Inequalities involving functions and their integrals and derivatives. Netherlands: Springer Science & Business Media; 1991.
   Google Scholar
• Kavian O. Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Mathématiques et Applications. Springer-Verlag; 1993.
   Google Scholar
• Appell J, Zabrejko PP. Nonlinear superposition operators. Cambridge: Cambridge University Press; 1990.
   Google Scholar