The role of a strong confining potential in a nonlinear Fokker–Planck equation

[1]  Yves Capdeboscq,et al.  Stability estimates for systems with small cross-diffusion, , 2018, 1801.06470.

[2]  Markus Schmidtchen,et al.  Zoology of a Nonlocal Cross-Diffusion Model for Two Species , 2017, SIAM J. Appl. Math..

[3]  Zheng Sun,et al.  A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials , 2017, J. Comput. Phys..

[4]  S. Jonathan Chapman,et al.  Diffusion of Particles with Short-Range Interactions , 2017, SIAM J. Appl. Math..

[5]  J. Carrillo,et al.  The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime , 2016, 1612.08225.

[6]  Symmetry breaking in clogging for oppositely driven particles. , 2015, Physical review. E.

[7]  Inwon C. Kim,et al.  A Fokker-Planck type approximation of parabolic PDEs with oblique boundary data , 2015 .

[8]  G. Pavliotis,et al.  Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations , 2015, 1505.01571.

[9]  J. Carrillo,et al.  A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure , 2014, 1402.4252.

[10]  Lorenzo Pareschi,et al.  Reviews , 2014 .

[11]  A. Moussa.  Some variants of the classical Aubin–Lions Lemma , 2014, 1401.7231.

[12]  Ansgar Jüngel,et al.  A Note on Aubin-Lions-Dubinskiĭ Lemmas , 2013, 1305.6235.

[13]  Chun Liu,et al.  PNP equations with steric effects: a model of ion flow through channels. , 2012, The journal of physical chemistry. B.

[14]  Michel Cristofol,et al.  Inverse Problem for a Curved Quantum Guide , 2012, Int. J. Math. Math. Sci..

[15]  Francis Filbet,et al.  A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations , 2011, SIAM J. Sci. Comput..

[16]  Maria Bruna,et al.  Excluded-volume effects in the diffusion of hard spheres. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Burger,et al.  Continuous limit of a crowd motion and herding model: Analysis and numerical simulations , 2011 .

[18]  Eric Carlen,et al.  Functional inequalities, thick tails and asymptotics for the critical mass Patlak–Keller–Segel model , 2010, 1009.0134.

[19]  Andrea L. Bertozzi,et al.  Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion , 2010 .

[20]  J. Carrillo,et al.  Double milling in self-propelled swarms from kinetic theory , 2009 .

[21]  K. Painter,et al.  A User's Guide to Pde Models for Chemotaxis , 2022 .

[22]  José A. Carrillo,et al.  Volume effects in the Keller-Segel model : energy estimates preventing blow-up , 2006 .

[23]  G. Toscani.  Kinetic models of opinion formation , 2006, math-ph/0605052.

[24]  C. Villani,et al.  Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media , 2006 .

[25]  Darryl D. Holm,et al.  Formation of clumps and patches in self-aggregation of finite-size particles , 2005, nlin/0506020.

[26]  A. Bertozzi,et al.  A Nonlocal Continuum Model for Biological Aggregation , 2005, Bulletin of mathematical biology.

[27]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[28]  C. Villani,et al.  Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates , 2003 .

[29]  Thierry Gallouët,et al.  Convergence of a finite volume scheme for nonlinear degenerate parabolic equations , 2002, Numerische Mathematik.

[30]  Ansgar Jüngel,et al.  Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities , 2001 .

[31]  F. Otto.  THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION , 2001 .

[32]  Giuseppe Toscani,et al.  ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS , 2001 .

[33]  Giuseppe Toscani,et al.  Exponential convergence toward equilibrium for homogeneous Fokker–Planck‐type equations , 1998 .

[34]  Emanuele Caglioti,et al.  A Non-Maxwellian Steady Distribution for One-Dimensional Granular Media , 1998 .

[35]  E. Caglioti,et al.  A kinetic equation for granular media , 2009 .

[36]  D. Kinderlehrer,et al.  THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .

[37]  O. A. Ladyzhenskai︠a︡,et al.  Linear and Quasi-linear Equations of Parabolic Type , 1995 .

[38]  Peter Szmolyan,et al.  A system of convection—diffusion equations with small diffusion coefficient arising in semiconductor physics , 1989 .

[39]  Peter A. Markowich,et al.  The Stationary Semiconductor Device Equations. , 1987 .

[40]  Stephan Luckhaus,et al.  Quasilinear elliptic-parabolic differential equations , 1983 .

[41]  G. Stampacchia,et al.  Inverse Problem for a Curved Quantum Guide , 2012, Int. J. Math. Math. Sci..