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科学研究
报告题目:

Analytic smoothing effect of a class of ultra-parabolic equations

报告人:

徐超江教授 (南京航空航天大学)

报告时间:

报告地点:

理学院东北楼四楼报告厅(404)

报告摘要:

We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the analytic smoothing effect of Cauchy problem, that means, for the initial datum belongs to $L^2$, we prove that the solution is analytic for all spatial variables when $t>0$. This class operators contains many kinetic operators such as, Kolmogorov-Fakker-Planck operators, Landau operators and non-cuttoff Boltzmann operators.

To overcome the degeneracy in the spatial variable, a family of well-chosen vector fields with time-dependent coefficients will play a crucial role, and the analytic regularization effect of weak solutions relies on a quantitative estimate on directional derivatives in these vector fields.