Existence result for the one-dimensional full model of phase transitions. (English) Zbl 1003.80003
Summary: This note deals with a nonlinear system of partial differential equations accounting for phase transition phenomena. The existence of solutions to a Cauchy-Neumann problem is established in the one-dimensional space setting, using a regularization – a priori estimates – passage to limit procedure.
MSC:
| 80A22 | Stefan problems, phase changes, etc. |
| 35K55 | Nonlinear parabolic equations |
| 35B50 | Maximum principles in context of PDEs |
References:
| [1] | Attouch, H.: Variational Convergence for Functions and Operators. London: Pitman 1984. · Zbl 0561.49012 |
| [2] | Baiocchi, C.: Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert. Ann. Mat. Pura Appl. (4) 76 (1967), 233 - 304. · Zbl 0153.17202 · doi:10.1007/BF02412236 |
| [3] | Barbu, V.: Nonlinear Semigroups and Differential Equations in Banach Spaces. Leyden: Noordhoff 1976. · Zbl 0328.47035 |
| [4] | Bonfanti, G., Frémond, M. and F. Luterotti: Global solution to a nonlinear system for irreversible phase changes. Adv. Math. Sci. Appl. 10 (2000), 1 -24. · Zbl 0956.35122 |
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