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In this paper, hypocoercivity methods are applied to linear kinetic equations with mass conservation and without confinement, in order to prove that the solutions have an algebraic decay rate in the long-time range, which the same as the rate of the heat equation.
Zufällige Bewegungen (zur Theorie der Brownschen Bewegung)
Kolmogoroff, A · 1934
Earlier work this paper cites.
A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems
Bhatnagar, P. L., Gross, E. P., and Krook, M · 1954
Earlier work this paper cites.
Continuity of solutions of parabolic and elliptic equations
Nash, J · 1958
Earlier work this paper cites.
On the equations of Brownian motion
Il ′ \prime in, A. M., and Has ′ \prime minskiĭ, R. Z · 1964
Earlier work this paper cites.
Hypoelliptic second order differential equations
Hörmander, L · 1967
Earlier work this paper cites.
Methods of modern mathematical physics. I
Reed, M., and Simon, B · 1980
Earlier work this paper cites.
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Beckner, W · 1989
Earlier work this paper cites.
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Kawashima, S · 1990
Earlier work this paper cites.
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Victory, Jr., H. D., and O’Dwyer, B. P · 1990
Earlier work this paper cites.
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Bouchut, F · 1993
Earlier work this paper cites.
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Glassey, R. T · 1996
Earlier work this paper cites.
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Earlier work this paper cites.
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