Free Access
Issue |
ESAIM: COCV
Volume 22, Number 2, April-June 2016
|
|
---|---|---|
Page(s) | 473 - 499 | |
DOI | https://doi.org/10.1051/cocv/2015014 | |
Published online | 18 March 2016 |
- V. Barbu, Optimal Control of Variational Inequalities. In vol. 100 of Res. Notes Math. Pitman, Advanced Publishing Program, Boston, MA (1984). [Google Scholar]
- V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces. Springer Monogr. Math. Springer, New York (2010). [Google Scholar]
- P. Colli and Ph. Laurençot, Weak solutions to the Penrose−Fife phase field model for a class of admissible heat flux laws. Phys. D 111 (1998) 311–334. [CrossRef] [MathSciNet] [Google Scholar]
- P. Colli and J. Sprekels, On a Penrose−Fife model with zero interfacial energy leading to a phase-field system of relaxed Stefan type. Ann. Mat. Pura Appl. 169 (1995) 269–289. [CrossRef] [MathSciNet] [Google Scholar]
- P. Colli and J. Sprekels, Stefan problems and the Penrose−Fife phase field model. Adv. Math. Sci. Appl. 7 (1997) 911–934. [MathSciNet] [Google Scholar]
- P. Colli, Ph. Laurençot and J. Sprekels, Global solution to the Penrose−Fife phase field model with special heat flux laws, Variations of domain and free-boundary problems in solid mechanics (Paris, 1997) 181–188; Vol. 66. of Solid Mech. Appl. Kluwer Acad. Publ., Dordrecht (1999). [Google Scholar]
- P. Colli, D. Hilhorst, F. Issard-Roch and G. Schimperna, Long time convergence for a class of variational phase-field models, Discrete Contin. Dyn. Syst. 25 (2009) 63–81. [CrossRef] [MathSciNet] [Google Scholar]
- M. Fabrizio, A. Favini and G. Marinoschi, An optimal control problem for a singular system of solid-liquid transition. Numer. Funct. Anal. Optim. 31 (2010) 989–1022. [CrossRef] [MathSciNet] [Google Scholar]
- E. Feireisl and G. Schimperna, Large time behaviour of solutions to Penrose−Fife phase change models. Math. Methods Appl. Sci. 28 (2005) 2117–2132. [CrossRef] [MathSciNet] [Google Scholar]
- W. Horn, J. Sokołowski and J. Sprekels, A control problem with state constraints for a phase-field model. Control Cybernet 25 (1996) 1137–1153. [MathSciNet] [Google Scholar]
- W. Horn, J. Sprekels and S. Zheng, Global existence of smooth solutions to the Penrose−Fife model for Ising ferromagnets. Adv. Math. Sci. Appl. 6 (1996) 227–241. [MathSciNet] [Google Scholar]
- A. Ito and N. Kenmochi, Inertial set for a phase transition model of Penrose−Fife type. Adv. Math. Sci. Appl. 10 (2000) 353–374; Correction in Adv. Math. Sci. Appl. 11 (2001) 481. [MathSciNet] [Google Scholar]
- Ph. Laurençot, Étude de quelques problèmes aux dérivées partielles non linéaires. Thèse de l’Université de France-Comté, Besançon (1993). [Google Scholar]
- Ph. Laurençot, Solutions to a Penrose−Fife model of phase-field type. J. Math. Anal. Appl. 185 (1994) 262–274. [CrossRef] [MathSciNet] [Google Scholar]
- Ph. Laurençot, Weak solutions to a Penrose−Fife model for phase transitions. Adv. Math. Sci. Appl. 5 (1995) 117–138. [MathSciNet] [Google Scholar]
- J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris (1969). [Google Scholar]
- A. Miranville, E. Rocca, G. Schimperna and A. Segatti, The Penrose−Fife phase-field model with coupled dynamic boundary conditions. Discrete Contin. Dyn. Syst. 34 (2014) 4259–4290. [CrossRef] [MathSciNet] [Google Scholar]
- J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris – Academia, Praha (1967). [Google Scholar]
- L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa 13 (1959) 115–162. [MathSciNet] [Google Scholar]
- O. Penrose and P.C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Phys. D 43 (1990) 44–62. [Google Scholar]
- O. Penrose and P.C. Fife, On the relation between the standard phase-field model and a “thermodynamically consistent” phase-field mode. Phys. D 69 (1993) 107–113. [CrossRef] [MathSciNet] [Google Scholar]
- E. Rocca and G. Schimperna, Universal attractor for some singular phase transition systems. Phys. D 192 (2004) 279–307. [CrossRef] [MathSciNet] [Google Scholar]
- G. Schimperna, Global and exponential attractors for the Penrose−Fife system. Math. Models Methods Appl. Sci. 19 (2009) 969–991. [CrossRef] [MathSciNet] [Google Scholar]
- G. Schimperna, A. Segatti and S. Zelik, Asymptotic uniform boundedness of energy solutions to the Penrose−Fife model. J. Evol. Equ. 12 (2012) 863–890. [Google Scholar]
- J. Sprekels and S.M. Zheng, Optimal control problems for a thermodynamically consistent model of phase-field type for phase transitions. Adv. Math. Sci. Appl. 1 (1992) 113–125. [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.