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We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law.
Carlo Cattaneo, Sulla conduzione del calore , Atti Sem. Mat. Fis. Univ. Modena 3
1949
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1960
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Seiji Ukai, On the existence of global solutions of mixed problem for non-linear Boltzmann equation , Proc. Japan Acad. 50
1974
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Ammon Pazy, Semigroups of linear operators and applications to partial differential equations , Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR MR710486 (85g:47061)
1983
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P. Degond, T. Goudon, and F. Poupaud, Diffusion limit for nonhomogeneous and non-micro-reversible processes , Indiana Univ. Math. J. 49
2000
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L. Desvillettes and C. Villani, On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: the linear Fokker-Planck equation , Comm. Pure Appl. Math. 54
2001
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Yan Guo, The Landau equation in a periodic box , Comm. Math. Phys. 231
2002
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by same author, The Vlasov-Poisson-Boltzmann system near Maxwellians , Comm. Pure Appl. Math. 55
2002
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Maria J. Cáceres, José A. Carrillo, and Thierry Goudon, Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles , Comm. Partial Differential Equations 28
2003
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by same author, Classical solutions to the Boltzmann equation for molecules with an angular cutoff , Arch. Ration. Mech. Anal. 169
2003
Earlier work this paper cites.
by same author, The Vlasov-Maxwell-Boltzmann system near Maxwellians , Invent. Math. 153
2003
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Klemens Fellner, Lukas Neumann, and Christian Schmeiser, Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes , Monatsh. Math. 141
2004
Earlier work this paper cites.
by same author, The Boltzmann equation in the whole space , Indiana Univ. Math. J. 53
2004
Cited alongside, same era.
Frédéric Hérau and Francis Nier, Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential , Arch. Ration. Mech. Anal. 171
2004
Cited alongside, same era.
Tai-Ping Liu and Shih-Hsien Yu, Boltzmann equation: micro-macro decompositions and positivity of shock profiles , Comm. Math. Phys. 246
2004
Cited alongside, same era.
Robert M. Strain and Yan Guo, Stability of the relativistic Maxwellian in a collisional plasma , Comm. Math. Phys. 251
2004
Cited alongside, same era.
by same author, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation , Invent. Math. 159
2005
Cited alongside, same era.
Ming-Yi Lee, Tai-Ping Liu, and Shih-Hsien Yu, Large-time behavior of solutions for the Boltzmann equation with hard potentials , Comm. Math. Phys. 269
2007
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by same author, Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation , Comm. Pure Appl. Math. 60
2007
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Dominique Bakry, Franck Barthe, Patrick Cattiaux, and Arnaud Guillin, A simple proof of the Poincaré inequality for a large class of probability measures including the log-concave case , Electron. Commun. Probab. 13
2008
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by same author, Exponential decay for soft potentials near Maxwellian , Arch. Ration. Mech. Anal. 187
2008
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Cédric Villani, Hypocoercivity , To appear in Memoirs Amer. Math. Soc., 2008
2008
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Frédéric Hérau, Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation , Asymptot. Anal. 46
2006
Cited alongside, same era.
Clément Mouhot and Lukas Neumann, Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus , Nonlinearity 19
2006
Cited alongside, same era.
by same author, Almost exponential decay near Maxwellian , Comm. Partial Differential Equations 31
2006
Cited alongside, same era.
Shih-Hsien Yu, The development of the Green’s function for the Boltzmann equation , J. Stat. Phys. 124
2006
Cited alongside, same era.
Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, and Juan-Luis Vázquez, Hardy-Poincaré inequalities and applications to nonlinear diffusions , Comptes Rendus Mathématique 344
2007
Cited alongside, same era.
Jean Dolbeault, Peter Markowich, Dietmar Ölz, and Christian Schmeiser, Non linear diffusions as limit of kinetic equations with relaxation collision kernels , Arch. Ration. Mech. Anal. 186
2007
Cited alongside, same era.
Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, and Juan-Luis Vázquez, Asymptotics of the fast diffusion equation via entropy estimates , Archive for Rational Mechanics and Analysis 191
2009
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Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, and Juan-Luis Vázquez, Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities , Preprint hal-00404718, 2009
2009
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Jean Dolbeault, Clément Mouhot, and Christian Schmeiser, Hypocoercivity for kinetic equations with linear relaxation terms , Comptes Rendus Mathematique 347
2009
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by same author, Hypocoercivity for linear kinetic equations , In preparation, 2010
2010
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2010
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M. Hitrik and K. Pravda-Starov, Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics , To appear in Communications in Partial Differential Equations, 2010
2010
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