Asymptotic behavior of degenerate linear transport equations

Bulletin des Sciences Mathématiques - Tập 133 - Trang 848-858 - 2009
Laurent Desvillettes1, Francesco Salvarani2
1CMLA, ENS Cachan, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt. Wilson, 94235 Cachan Cedex, France
2Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata, 1, 27100 Pavia, Italy

Tài liệu tham khảo

Desvillettes, 2006, Hypocoercivity: The example of linear transport, vol. 409, 33 Desvillettes, 2007, Entropy methods for reaction–diffusion systems: Degenerate diffusion, Discrete Contin. Dyn. Syst., supplement, 304 Desvillettes, 2001, On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker–Planck equation, Comm. Pure Appl. Math., 54, 1, 10.1002/1097-0312(200101)54:1<1::AID-CPA1>3.0.CO;2-Q Desvillettes, 2005, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation, Invent. Math., 105, 245, 10.1007/s00222-004-0389-9 Goldstein, 1951, On diffusion by discontinuous movements, and on the telegraph equation, Quart. J. Mech. Appl. Math., 4, 129, 10.1093/qjmam/4.2.129 Hérau, 2006, Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation, Asymptot. Anal., 46, 349 Mouhot, 2006, Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus, Nonlinearity, 19, 969, 10.1088/0951-7715/19/4/011 Taylor, 1922, Diffusion by continuous movements, Proc. London Math. Soc., 20, 196, 10.1112/plms/s2-20.1.196 Villani, 2006, Hypocoercive diffusion operators, 473