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Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on $R^d$ are studied.
De Giorgi, E. New problems on minimizing movements
1983
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Angenent, S. B. Large time asymptotics for the porous medium equation, pages 21–34 in Nonlinear diffusion equations and their equilibrium states I
1988
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Bernis, F.; Friedman, A. Higher order nonlinear degenerate parabolic equations
1990
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Derrida, B.; Lebowitz, J. L.; Speer, E. R.; Spohn, H. Dynamics of an anchored Toom interface
1991
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Derrida, B.; Lebowitz, J. L.; Speer, E. R.; Spohn, H. Fluctuations of a stationary nonequilibrium interface
1991
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Bleher, P. M.; Lebowitz, J. L.; Speer, E. R. Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations
1994
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Almgren, R.; Bertozzi, A.; Brenner, M. Stable and unstable singularities in the unforced Hele-Shaw cell
1996
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McCann, R.J. A convexity principle for interacting gases
1997
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Bertsch, M.; Dal Passo, R.; Garcke, H.; Grün, G. The thin viscous flow equation in higher space dimensions
1998
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Dal Passo, R.; Garcke, H.; Grün, G. On a fourth-order degenerate parabolic equation: global entropy estimates, existence, and qualitative behavior of solutions
1998
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Jordan, R.; Kinderlehrer, D.; Otto, F. The variational formulation of the Fokker-Planck equation
1998
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Myers, T.G. Thin films with high surface tension
1998
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Carrillo, J. A.; Toscani, G. Asymptotic L 1 L^{1} -decay of solutions of the porous medium equation to self-similarity
2000
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Jüngel, A.; Pinnau, René. Global nonnegative solutions of a nonlinear fourth-order parabolic equation for quantum systems
2000
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Otto, F. and Villani, C. Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
2000
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Carrillo, J. A.; Jüngel, A.; Markowich, P. A.; Toscani, G.; Unterreiter, A. Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
2001
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Giacomelli L., Otto F. Variational formulation for the lubrication approximation of the Hele-Shaw flow
2001
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Denzler, J.; McCann, R. J. Fast diffusion to self-similarity: complete spectrum, long-time asymptotics, and numerology
2005
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Sturm, K.-T. Convex functionals of probability measures and nonlinear diffusions on manifolds
2005
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Sturm, K.-T. and von Renesse, M.-K. Transport inequalities, gradient estimates, entropy and Ricci curvature
2005
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Ambrosio, L.; Savaré, G. Gradient flows of probability measures
2006
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Carrillo, J. A.; McCann, R. J. and Villani, C. Contractions in the 2 2 -Wasserstein length space and thermalization of granular media
2006
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Jüngel, A.; Matthes, D. An algorithmic construction of entropies in higher-order nonlinear PDEs
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Otto, F. The geometry of dissipative evolution equations: the porous medium equation
2001
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Carrillo, J. A.; Toscani, G. Long-time asymptotics for strong solutions of the thin film equation
2002
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Del Pino, M.; Dolbeault, J. Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
2002
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Villani, C. Topics in optimal transportation
2003
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Grün, G. Droplet spreading under weak slippage—existence for the Cauchy problem
2004
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Ambrosio, L.; Gigli, N.; Savaré, G. Gradient flows in metric spaces and in the space of probability measures
2005
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Becker, J.; Grün, G. The thin-film equation: recent advances and some new perspectives
2005
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2006
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Carlen, E. A.; Ulusoy, S. Asymptotic equipartition and long time behavior of solutions of a thin-film equation
2007
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Vázquez, J. L. The porous medium equation. Mathematical theory
2007
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Denzler, J.; McCann, R. J. Nonlinear diffusion from a delocalized source: affine self-similarity, time reversal, & nonradial focusing geometries
2008
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Gianazza, U.; Savaré, G.; Toscani, G. The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation
2009
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Jüngel, A.; Matthes, D. The Derrida-Lebowitz-Speer-Spohn equation: existence, non-uniqueness, and decay rates of the solutions
2015
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Otto, F. Lubrication approximation with prescribed nonzero contact angle: An existence result
2077
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