# zbMATH — the first resource for mathematics

Averaging lemmas without time Fourier transform and application to discretized kinetic equations. (English) Zbl 0933.35159
The authors present modified proofs of averaging lemmas for kinetic equations. These proofs are based on Fourier transforms with respect to $$x$$ and $$v$$, but not $$t$$. The method is then used to prove estimates on time averages of discrete (in time) approximations of kinetic equations.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 82C40 Kinetic theory of gases in time-dependent statistical mechanics
Full Text:
##### References:
 [1] DOI: 10.1002/cpa.3160420603 · Zbl 0698.35128 [2] DOI: 10.1142/S0218202596000444 · Zbl 0876.35088 [3] Bézard, Bull. Soc. Math. France 122 pp 29– (1994) · Zbl 0798.35025 [4] Perthame, Ann. Scient. Ecole Normale Supérieure 4 31 pp 591– (1998) · Zbl 0956.45010 [5] DOI: 10.1002/mma.1670130508 · Zbl 0717.35017 [6] DOI: 10.1090/S0894-0347-1994-1201239-3 [7] DiPerna, Ann. I.H.P., Analyse non-linéaire 8 pp 271– (1991) · Zbl 0763.35014 [8] Golse, Asympt. Analysis 6 pp 135– (1992) [9] Lions, C. R. Acad. Sci. Série I 320 pp 911– (1995) [10] Golse, C. R. Acad. Sci. Série I 301 pp 341– (1985) [11] DOI: 10.1016/0022-1236(88)90051-1 · Zbl 0652.47031 [12] Golse, Rend. Sem. Mat. Univ. Pol. Torino, Fasdcolo Speciale 1988 ’Hyperbolic Equations’ pp 101– (1987) [13] DOI: 10.1080/03605309108820822 · Zbl 0770.35001 [14] Lions, C. R. Acad. Sci. Série I 314 pp 801– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.