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arXiv:0903.3703 [math.AP]AbstractReferencesReviewsResources

Ultra-analytic effect of Cauchy problem for a class of kinetic equations

Yoshinori Morimoto, Chao-Jiang Xu

Published 2009-03-22Version 1

The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra-analytic effects of the Cauchy problem. Those smoothing effect results are optimal and similar to heat equation. In the second part, we study a model of spatially inhomogeneous linear Landau equation with Maxwellian molecules, and show the analytic effect of the Cauchy problem.

Comments: 22 pages, to appear in JDE
Journal: J. Differential Equations 247 (2009) 597-617
Categories: math.AP
Subjects: 35A05, 35B65, 35D10, 35H20
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