-
Previous Article
Equilibrium and stability of tensegrity structures: A convex analysis approach
- DCDS-S Home
- This Issue
-
Next Article
Parabolic quasi-variational diffusion problems with gradient constraints
Well-posedness of an extended model for water-ice phase transitions
1. | Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1 |
2. | WIAS Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano |
References:
[1] |
C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J. 44(119) (1994), 109-140. |
[2] |
M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions," Appl. Math. Sci. 121, Springer, New York, 1996. |
[3] |
P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys, Quart. Appl. Math., 48 (1990), 31-47. |
[4] |
P. Colli, P. Krejčí, E. Rocca and J. Sprekels, A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity, J. Differ. Equations, 251 (2011), 1354-1387. |
[5] |
M. Frémond, "Non-Smooth Thermomechanics," Springer-Verlag Berlin, 2002. |
[6] |
M. Frémond and E. Rocca, Well-posedness of a phase transition model with the possibility of voids, Math. Models Methods Appl. Sci., 16 (2006), 559-586.
doi: 10.1142/S0218202506001261. |
[7] |
M. Frémond and E. Rocca, Solid liquid phase changes with different densities, Q. Appl. Math., 66 (2008), 609-632. |
[8] |
V. Girault and P.-A. Raviart, "Finite Element Methods for Navier-Stokes Equations," Springer-Verlag, Berlin, 1986. |
[9] |
G. Joos, "Lehrbuch der Theoretischen Physik," Akademische Verlagsgesellschaft, Leipzig 1939 (In German). |
[10] |
P. Krejčí, E. Rocca and J. Sprekels, A bottle in a freezer, SIAM J. Math. Anal., 41 (2009), 1851-1873.
doi: 10.1137/09075086X. |
[11] |
P. Krejčí, E. Rocca and J. Sprekels, Phase separation in a gravity field, Discrete Contin. Dyn. Syst. Ser. S, 4, (2011), 391-407.
doi: 10.3934/dcdss.2011.4.391. |
[12] |
P. Krejčí, E. Rocca and J. Sprekels, Liquid-solid phase transitions in a deformable container, Contribution to the book "Continuous Media with Microstructure'' on the occasion of Krzysztof Wilmanski's 70th birthday, Springer, (2010), 285-300. |
[13] |
E. Madelung, "Die mathematischen Hilfsmittel des Physikers," Sixth Edition, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957. (In German). |
[14] |
A. Visintin, "Models of Phase Transitions," Progress in Nonlinear Differential Equations and their Applications 28, Birkhäuser Boston, 1996. |
show all references
References:
[1] |
C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J. 44(119) (1994), 109-140. |
[2] |
M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions," Appl. Math. Sci. 121, Springer, New York, 1996. |
[3] |
P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys, Quart. Appl. Math., 48 (1990), 31-47. |
[4] |
P. Colli, P. Krejčí, E. Rocca and J. Sprekels, A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity, J. Differ. Equations, 251 (2011), 1354-1387. |
[5] |
M. Frémond, "Non-Smooth Thermomechanics," Springer-Verlag Berlin, 2002. |
[6] |
M. Frémond and E. Rocca, Well-posedness of a phase transition model with the possibility of voids, Math. Models Methods Appl. Sci., 16 (2006), 559-586.
doi: 10.1142/S0218202506001261. |
[7] |
M. Frémond and E. Rocca, Solid liquid phase changes with different densities, Q. Appl. Math., 66 (2008), 609-632. |
[8] |
V. Girault and P.-A. Raviart, "Finite Element Methods for Navier-Stokes Equations," Springer-Verlag, Berlin, 1986. |
[9] |
G. Joos, "Lehrbuch der Theoretischen Physik," Akademische Verlagsgesellschaft, Leipzig 1939 (In German). |
[10] |
P. Krejčí, E. Rocca and J. Sprekels, A bottle in a freezer, SIAM J. Math. Anal., 41 (2009), 1851-1873.
doi: 10.1137/09075086X. |
[11] |
P. Krejčí, E. Rocca and J. Sprekels, Phase separation in a gravity field, Discrete Contin. Dyn. Syst. Ser. S, 4, (2011), 391-407.
doi: 10.3934/dcdss.2011.4.391. |
[12] |
P. Krejčí, E. Rocca and J. Sprekels, Liquid-solid phase transitions in a deformable container, Contribution to the book "Continuous Media with Microstructure'' on the occasion of Krzysztof Wilmanski's 70th birthday, Springer, (2010), 285-300. |
[13] |
E. Madelung, "Die mathematischen Hilfsmittel des Physikers," Sixth Edition, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957. (In German). |
[14] |
A. Visintin, "Models of Phase Transitions," Progress in Nonlinear Differential Equations and their Applications 28, Birkhäuser Boston, 1996. |
[1] |
Emil Minchev. Existence and uniqueness of solutions of a system of nonlinear PDE for phase transitions with vector order parameter. Conference Publications, 2005, 2005 (Special) : 652-661. doi: 10.3934/proc.2005.2005.652 |
[2] |
Luis F. López, Yannick Sire. Rigidity results for nonlocal phase transitions in the Heisenberg group $\mathbb{H}$. Discrete and Continuous Dynamical Systems, 2014, 34 (6) : 2639-2656. doi: 10.3934/dcds.2014.34.2639 |
[3] |
Monica Marras, Stella Vernier Piro. On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients. Conference Publications, 2013, 2013 (special) : 535-544. doi: 10.3934/proc.2013.2013.535 |
[4] |
J. R. L. Webb. Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 177-186. doi: 10.3934/dcdss.2008.1.177 |
[5] |
Honghu Liu. Phase transitions of a phase field model. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 883-894. doi: 10.3934/dcdsb.2011.16.883 |
[6] |
Lorenzo Brasco, Marco Squassina, Yang Yang. Global compactness results for nonlocal problems. Discrete and Continuous Dynamical Systems - S, 2018, 11 (3) : 391-424. doi: 10.3934/dcdss.2018022 |
[7] |
Tong Yang, Fahuai Yi. Global existence and uniqueness for a hyperbolic system with free boundary. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 763-780. doi: 10.3934/dcds.2001.7.763 |
[8] |
Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825 |
[9] |
Shu-Yi Zhang. Existence of multidimensional non-isothermal phase transitions in a steady van der Waals flow. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2221-2239. doi: 10.3934/dcds.2013.33.2221 |
[10] |
G. Kamberov. Prescribing mean curvature: existence and uniqueness problems. Electronic Research Announcements, 1998, 4: 4-11. |
[11] |
A. Jiménez-Casas. Invariant regions and global existence for a phase field model. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 273-281. doi: 10.3934/dcdss.2008.1.273 |
[12] |
Shaoqiang Tang, Huijiang Zhao. Stability of Suliciu model for phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (4) : 545-556. doi: 10.3934/cpaa.2004.3.545 |
[13] |
Tatyana S. Turova. Structural phase transitions in neural networks. Mathematical Biosciences & Engineering, 2014, 11 (1) : 139-148. doi: 10.3934/mbe.2014.11.139 |
[14] |
Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio. Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1801-1816. doi: 10.3934/dcdsb.2017107 |
[15] |
Shihui Zhu. Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 5201-5221. doi: 10.3934/dcds.2016026 |
[16] |
Hiroshi Matano, Yoichiro Mori. Global existence and uniqueness of a three-dimensional model of cellular electrophysiology. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1573-1636. doi: 10.3934/dcds.2011.29.1573 |
[17] |
Gabriele Bonanno, Pasquale Candito, Roberto Livrea, Nikolaos S. Papageorgiou. Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1169-1188. doi: 10.3934/cpaa.2017057 |
[18] |
Mingxin Wang. Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 415-421. doi: 10.3934/dcdsb.2018179 |
[19] |
Mingxin Wang. Erratum: Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021269 |
[20] |
Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. Global existence for a two-phase flow model with cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 957-979. doi: 10.3934/dcdsb.2019198 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]