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1. | Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1, Czech Republic |
2. | WIAS Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano |
3. | Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin |
References:
[1] |
M. Brokate, J. Sprekels, "Hysteresis and Phase Transitions," Appl. Math. Sci., 121, Springer, New York, 1996. |
[2] |
P. Colli, M. Frémond and A Visintin, Thermo-mechanical evolution of shape memory alloys, Quart. Appl. Math., 48 (1990), 31-47. |
[3] |
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.
doi: 10.3934/dcds.2009.25.63. |
[4] |
M. Frémond, "Non-Smooth Thermo-Mechanics," Springer-Verlag, Berlin, 2002. |
[5] |
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. |
[6] |
M. Frémond and E. Rocca, Solid liquid phase changes with different densities, Q. Appl. Math., 66 (2008), 609-632. |
[7] |
V. Girault and P.-A. Raviart, "Finite Element Methods for Navier-Stokes Equations," Springer-Verlag, Berlin, 1986. |
[8] |
P. Krejčí, Hysteresis operators-A new approach to evolution differential inequalities, Comment. Math. Univ. Carolinae, 33 (1989), 525-536. |
[9] |
P. Krejčí, E. Rocca and J. Sprekels, A bottle in a freezer, SIAM J. Math. Anal., 41 (2009), 1851-1873.
doi: 10.1137/09075086X. |
[10] |
P. Krejčí, Elastoplastic reaction of a container to water freezing, Mathematica Bohemica, to appear (2010). |
[11] |
P. Krejčí, J. Sprekels and U. Stefanelli, Phase-field models with hysteresis in one-dimensional thermoviscoplasticity, SIAM J. Math. Anal., 34 (2002), 409-434.
doi: 10.1137/S0036141001387604. |
[12] |
P. Krejčí, J. Sprekels and U. Stefanelli, One-dimensional thermo-visco-plastic processes with hysteresis and phase transitions, Adv. Math. Sci. Appl., 13 (2003), 695-712. |
[13] |
E. Rocca and R. Rossi, A nonlinear degenerating PDE system modelling phase transitions in thermoviscoelastic materials, J. Differential Equations, 245 (2008), 3327-3375.
doi: 10.1016/j.jde.2008.02.006. |
[14] |
E. Rocca and R. Rossi, Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials, Appl. Math., 53 (2008), 485-520.
doi: 10.1007/s10492-008-0038-5. |
[15] |
A. Visintin, "Models of Phase Transitions," Progress in Nonlinear Differential Equations and Their Applications, 28, Birkhäuser Boston, 1996. |
[16] |
H. Y. Erbil, "Surface Chemistry of Solid and Liquid Interfaces," Blackwell Publishing, John Wiley & Sons, 2006. |
show all references
References:
[1] |
M. Brokate, J. Sprekels, "Hysteresis and Phase Transitions," Appl. Math. Sci., 121, Springer, New York, 1996. |
[2] |
P. Colli, M. Frémond and A Visintin, Thermo-mechanical evolution of shape memory alloys, Quart. Appl. Math., 48 (1990), 31-47. |
[3] |
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.
doi: 10.3934/dcds.2009.25.63. |
[4] |
M. Frémond, "Non-Smooth Thermo-Mechanics," Springer-Verlag, Berlin, 2002. |
[5] |
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. |
[6] |
M. Frémond and E. Rocca, Solid liquid phase changes with different densities, Q. Appl. Math., 66 (2008), 609-632. |
[7] |
V. Girault and P.-A. Raviart, "Finite Element Methods for Navier-Stokes Equations," Springer-Verlag, Berlin, 1986. |
[8] |
P. Krejčí, Hysteresis operators-A new approach to evolution differential inequalities, Comment. Math. Univ. Carolinae, 33 (1989), 525-536. |
[9] |
P. Krejčí, E. Rocca and J. Sprekels, A bottle in a freezer, SIAM J. Math. Anal., 41 (2009), 1851-1873.
doi: 10.1137/09075086X. |
[10] |
P. Krejčí, Elastoplastic reaction of a container to water freezing, Mathematica Bohemica, to appear (2010). |
[11] |
P. Krejčí, J. Sprekels and U. Stefanelli, Phase-field models with hysteresis in one-dimensional thermoviscoplasticity, SIAM J. Math. Anal., 34 (2002), 409-434.
doi: 10.1137/S0036141001387604. |
[12] |
P. Krejčí, J. Sprekels and U. Stefanelli, One-dimensional thermo-visco-plastic processes with hysteresis and phase transitions, Adv. Math. Sci. Appl., 13 (2003), 695-712. |
[13] |
E. Rocca and R. Rossi, A nonlinear degenerating PDE system modelling phase transitions in thermoviscoelastic materials, J. Differential Equations, 245 (2008), 3327-3375.
doi: 10.1016/j.jde.2008.02.006. |
[14] |
E. Rocca and R. Rossi, Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials, Appl. Math., 53 (2008), 485-520.
doi: 10.1007/s10492-008-0038-5. |
[15] |
A. Visintin, "Models of Phase Transitions," Progress in Nonlinear Differential Equations and Their Applications, 28, Birkhäuser Boston, 1996. |
[16] |
H. Y. Erbil, "Surface Chemistry of Solid and Liquid Interfaces," Blackwell Publishing, John Wiley & Sons, 2006. |
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