Sobolev approximation for two-phase solutions of forward-backward parabolic problems
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G. Anzellotti, 1983, <em>Pairings between measures and functions and compensated compactness</em>,, Ann. Mat. Pura ed Appl., 135, 293, 10.1007/BF01781073
G. I. Barenblatt, 1993, <em>A degenerate pseudoparabolic regularization of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow</em>,, SIAM J. Math. Anal., 24, 1414, 10.1137/0524082
G. Bellettini, 2006, <em>A concept of solution and numerical experiments for forward-backward diffusion equations</em>,, Discrete Contin. Dyn. Syst., 16, 783, 10.3934/dcds.2006.16.783
K. Binder, 1986, <em>Kinetics of phase separation in the presence of slowly relaxing structural variables</em>,, J. Chem. Phys., 85, 1505, 10.1063/1.451190
M. Brokate, 1996, "Hysteresis and Phase Transitions,", Applied Mathematical Sciences, 121, 10.1007/978-1-4612-4048-8_5
G. Q. Chen, 1999, <em>Divergence-measure fields and hyperbolic conservation laws</em>,, Arch. Ration. Mech. Anal., 147, 89, 10.1007/s002050050146
A. De Pablo, 1991, <em>Regularity of solutions and interfaces of a generalized porous medium equation in $\mathbbR^N$</em>,, Ann. Mat. Pure Appl., 58, 51, 10.1007/BF01759299
L. C. Evans, 2004, <em>Irreversibility and hysteresis for a forward-backward diffusion equation</em>,, Math. Mod. Meth. Appl. Sci., 14, 1599, 10.1142/S0218202504003763
P. C. Fife, 2000, <em>Models for phase separation and their mathematics</em>,, Electron. J. Differential Equations, 48
H. L. Frisch, 1986, <em>Properties of a generalized diffusion equation with memory</em>,, J. Chem. Phys., 85, 1621, 10.1063/1.451204
M. E. Gurtin, 1996, <em>Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance</em>,, Phys. D, 92, 178, 10.1016/0167-2789(95)00173-5
M. Ghisi, 2007, <em>Gradient estimates for the Perona-Malik equation</em>,, Math. Ann., 337, 557, 10.1007/s00208-006-0047-1
B. H. Gilding, 2010, <em>The Riemann problem for a forward-backward parabolic equation</em>,, Phys. D, 239, 291, 10.1016/j.physd.2009.10.006
K. Höllig, 1983, <em>Existence of infinitely many solutions for a forward backward heat equation</em>,, Trans. Amer. Math. Soc., 278, 299, 10.2307/1999317
K. Höllig, 1983, <em>A diffusion equation with a nonmonotone constitutive function</em>,, in, 409
P. Lafitte, 2012, <em>Numerical exploration of a forward-backward diffusion equation</em>,, Math. Models Methods. Appl. Sci., 22, 10.1142/S0218202512500042
O. A. Ladyzenskaja, 1967, "Linear and Quasi-linear Equations of Parabolic Type,'', Translations of Mathematical Monographs, 23
H. Matano, 1982, <em>Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation</em>,, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 29, 401
C. Mascia, 2002, <em>Nonhomogeneous Dirichlet problems for degenerate parabolic-hyperbolic equation</em>,, Arch. Rational Mech. Anal., 163, 87, 10.1007/s002050200184
C. Mascia, 2007, <em>Evolution of stable phases in forward-backward parabolic equations</em>,, in, 47
C. Mascia, 2009, <em>Two-phase entropy solutions of a forward-backward parabolic equation</em>,, Arch. Ration. Mech., 194, 887, 10.1007/s00205-008-0185-6
A. Novick-Cohen, 1991, <em>Stable patterns in a viscous diffusion equation</em>,, Trans. Amer. Math. Soc., 324, 331, 10.1090/S0002-9947-1991-1015926-7
V. Padrón, 1998, <em>Sobolev regularization of a nonlinear ill-posed parabolic problem as a model for aggregating populations</em>,, Comm. Partial Differential Equations, 23, 457, 10.1080/03605309808821353
P. I. Plotnikov, 1994, <em>Passing to the limit with respect to viscosity in an equation with variable parabolicity direction</em>,, Diff. Equ., 30, 614
P. I. Plotnikov, 1993, <em>Equations with alternating direction of parabolicity and the hysteresis effect</em>,, Russian Acad. Sci., 47, 604
P. I. Plotnikov, 1999, <em>Forward-backward parabolic equations and hysteresis</em>,, J. Math. Sci., 93, 747, 10.1007/BF02366851
F. Smarrazzo, 2007, <em>On a class of equations with variable parabolicity direction</em>,, Discrete Contin. Dyn. Syst., 22, 729, 10.3934/dcds.2008.22.729
F. Smarrazzo, 2010, <em>Long-time behaviour of two-phase solutions to a class of forward-backward parabolic equations</em>,, Interface and Free Boundaries, 12, 369, 10.4171/IFB/239
F. Smarrazzo, 2010, <em>Long-time behaviour of solutions to a class of forward-backward parabolic equations</em>,, SIAM J. Math. Anal., 42, 1046, 10.1137/090763561
A. Terracina, 2011, <em>Qualitative behavior of the two-phase entropy solution of a forward-backward parabolic problem</em>,, SIAM J. Math. Anal., 43, 228, 10.1137/090778833
J. L. Vázquez, 2006, "Porous Medium Equation. Mathematical Theory,'', Oxford University Press
A. Visintin, 2002, <em>Forward-backward parabolic equations and hysteresis</em>,, Calc. Var. Partial Differential Equations, 15, 115, 10.1007/s005260100120