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References (38)
-
O. Ladyzhenskai︠a︡, V. Solonnikov, N. Uralʹt︠s︡eva (1995)
Linear and Quasi-linear Equations of Parabolic Type -
Songmu Zheng (1992)
Global existence for a thermodynamically consistent model of phase field typeDifferential and Integral Equations
-
Jan Pruess, M. Wilke (2010)
On Conserved Penrose-Fife Type ModelsarXiv: Analysis of PDEs
-
(1999)
Evolution equations generated by subdifferentials in the dual space of H1( ) -
N. Kenmochi (1990)
Neumann problems for a class of nonlinear degenerate parabolic equationsDifferential and Integral Equations
-
H. Brezis (1972)
Integrales convexes dans les espaces de SobolevIsrael Journal of Mathematics, 13
-
Nenad Dedic, L. Reyzin, Salil Vadhan (2002)
An Improved Pseudorandom Generator Based on Hardness of FactoringIACR Cryptol. ePrint Arch., 2002
-
S. Agmon, A. Douglis, L. Nirenberg (1959)
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I., CommPure Appl. Math., 12
-
G. Schimperna (2008)
Global and exponential attractors for the Penrose-Fife systemMathematical Models and Methods in Applied Sciences, 19
-
A. Damlamian, N. Kenmochi (1999)
Evolution equations generated by subdifferentials in the dual space of H 1 (Ω), Discrete ContinDynam. Systems., 5
-
G. Gilardi, A. Marson (2003)
On a Penrose–Fife type system with Dirichlet boundary conditions for temperatureMathematical Methods in the Applied Sciences, 26
-
H. Brezis, W. Strauss (1973)
Semi-linear second-order elliptic equations in L 1Journal of The Mathematical Society of Japan, 25
-
E. Rocca, G. Schimperna (2004)
Universal attractor for some singular phase transition systemsPhysica D: Nonlinear Phenomena, 192
-
N. Kenmochi, M. Niezgodka (1994)
Systems of nonlinear parabolic equations for phase change problems., 3
-
P. Laurençot (1998)
Weak solutions to a Penrose-Fife model with Fourier law for the temperatureJournal of Mathematical Analysis and Applications, 219
-
V. Barbu (1976)
Nonlinear Semigroups and di erential equations in Banach spaces -
(1977)
Caractérisation du sous-différentiel d’intégrandes convexes dans les espaces de Sobolev (French) -
(1979)
L p bounds of solutions of reaction-diffusion equations -
A. Ito, N. Kenmochi, M. Kubo (2003)
Non-isothermal phase transition models with Neumann boundary conditionsNonlinear Analysis-theory Methods & Applications, 53
-
P. Colli, G. Gilardi, E. Rocca, G. Schimperna (2004)
On a Penrose-Fife phase-field model with nonhomogeneous Neumann boundary conditions for the temperatureDifferential and Integral Equations
-
S. Agmon, A. Douglis, L. Nirenberg (1959)
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. ICommunications on Pure and Applied Mathematics, 12
-
J. Sprekels, S. Zheng (1993)
Global Smooth Solutions to a Thermodynamically Consistent Model of Phase-Field Type in Higher Space DimensionsJournal of Mathematical Analysis and Applications, 176
-
P. Laurençot (1994)
Solutions to a Penrose-Fife Model of Phase-Field TypeJournal of Mathematical Analysis and Applications, 185
-
V. Barbu, P. Colli, G. Gilardi, M. Grasselli (2000)
Existence, uniqueness, and longtime behavior for a nonlinear Volterra integrodifferential equationDifferential and Integral Equations
-
A. Miranville, S. Zelik (2004)
Robust exponential attractors for Cahn‐Hilliard type equations with singular potentialsMathematical Methods in the Applied Sciences, 27
-
O. Penrose, P. Fife (1990)
Thermodynamically consistent models of phase-field type for the kinetics of phase transitionsPhysica D: Nonlinear Phenomena, 43
-
J. Vázquez (2006)
Smoothing and decay estimates for nonlinear diffusion equations : equations of porous medium type -
H. Brezis, W.A. Strauss (1973)
Semi-linear second-order elliptic equations in L 1 , J.MathSoc. Japan., 25
-
(1987)
Compact sets in the space L p(0 -
P. Colli, P. Laurençot, J. Sprekels (1999)
Global Solution to the Penrose-Fife Phase Field Model with Special Heat Flux Laws -
R. Nochetto, Giuseppe Savaré (2006)
NONLINEAR EVOLUTION GOVERNED BY ACCRETIVE OPERATORS IN BANACH SPACES:: ERROR CONTROL AND APPLICATIONSMathematical Models and Methods in Applied Sciences, 16
-
C. Baiocchi (1967)
Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di HilbertAnnali di Matematica Pura ed Applicata, 76
-
M. Bonforte, J. Vázquez (2008)
Positivity, local smoothing, and Harnack inequalities for very fast diffusion equationsAdvances in Mathematics, 223
-
O. Penrose, P.C. Fife (1993)
On the relation between the standard phase-field model and a “thermodynamically consistent” phase-field modelPhys. D., 69
-
H. Brezis (1973)
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert -
E. Feireisl, G. Schimperna (2005)
Large time behaviour of solutions to Penrose–Fife phase change modelsMathematical Methods in the Applied Sciences, 28
-
P. Colli, Philippe Laurencçot (1998)
Weak solutions to the Penrose-Fife phase field model for a class of admissible heat flux lawsPhysica D: Nonlinear Phenomena, 111
-
R. Showalter (1996)
Monotone operators in Banach space and nonlinear partial differential equations
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Springer Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-012-0159-x
- Publisher site
- See Article on Publisher Site
Abstract
We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a unique solution under weak conditions on the initial data. Moreover, we prove asymptotic regularization properties of weak solutions.
Journal
Journal of Evolution Equations – Springer Journals
Published: Dec 1, 2012