Artículos de revistas
A Mathematical Analysis Of A Nonisothermal Allen-cahn Type System
Registro en:
Mathematical Methods In The Applied Sciences. , v. 35, n. 12, p. 1392 - 1405, 2012.
1704214
10.1002/mma.2504
2-s2.0-84864285040
Autor
Vaz C.L.D.
Boldrini J.L.
Institución
Resumen
Existence of solutions for a nonisothermal Allen-Cahn type system is proved by using a semidiscrete spectral Galerkin method together with degree theory and maximum principle. Regularity and uniqueness are obtained in a special situation for domains with dimension up to two and smooth enough data. The present system may model the evolution of solidification or melting processes occurring in certain binary alloys. Copyright © 2012 John Wiley & Sons, Ltd. 35 12 1392 1405 Beckermann, C., Diepers, H.J., Steinbach, I., Karma, A., Tong, X., Modeling melt convection in phase-field simulations of solidification (1999) Journal of Computational Physics, 154, pp. 468-496 Diepers, H.-J., Beckermann, C., Steinbach, I., Simulation of convection and ripening in a binary alloy mush using the phase-field method (1999) Acta Materialia, 47 (13), pp. 3663-3678. , DOI 10.1016/S1359-6454(99)00239-6 Boldrini, J.L., Caretta, B.C., Fernández-Cara, E., Analysis of a two-phase field model for the solidication of an alloy (2009) Journal of Mathematical Analysis and Applications, 357, pp. 25-44 Jiang, J., Convergence to equilibrium for a parabolic-hyperbolic phase field model with Cattaneo heat flux law (2008) Journal of Mathematical Analysis and Applications, 341, pp. 149-169 Rubio, P.M., Planas, G., Real, J., Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness (2009) Journal of Differential Equations, 246, pp. 4632-4652 Rappaz, J., Sheid, J.F., Existence of solutions to a phase-field model for the isothermal solidification process of binary alloy (2000) Mathematical Methods in the Applied Sciences, 23 (6), pp. 491-513 Moroşanu, C., Motreanu, D., A generalized phase-field system (1999) Journal of Mathematical Analysis and Applications, 273, pp. 515-540 Evans, L.C., (1998) Partial Differential Equations, , American Mathematical Society: Providence Ladyẑenskaja, O.A., Solonnikov, V.A., Ural'Ceva, N.N., Linear and quasilinear equations of parabolic type (1995) Translations of Mathematical Monographs, , American Mathematical Society: Providence Zheng, S., Nonlinear parabolic equations and hyperbolic-parabolic coupled system (1995) Pitman Monographs & Surveys in Pure & Applied Math, , Longman-Wiley: Essex Vaz, C.L.D., Boldrini, J.L., (2011) A Mathematical Analysis of A Non-isothermal Allen-Cahn Type System: Error Estimates, , pre-print, accepted for publication in the Mathematical Methods in the Applied Sciences Feng, X., Prohl, A., Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows (2003) Numerische Mathematik, 94 (1), pp. 33-65. , DOI 10.1007/s00211-002-0413-1 Deimling, K., (1984) Nonlinear Functional Analysis, , Springer-Verlag: Berlin Lions, J.L., (1987) Control of Distributed Singular Systems, , John Wiley & Sons Inc: New York Henry, D., Geometric theory of semilinear parabolic equations (1981) Lecture Notes in Mathematics, 840. , Springer-Verlag: Berlin