題目一：Bounded and compact Toeplitz operators with positive measure symbol on Fock type spaces

内容簡介：In this note, we discuss the Bergman projection and duality for Fock-type space Fp(1 ≤p < ∞) and Toeplitz operators Tμ with positive measure symbol μ between Fp(Cn) andFq(Cn) for 1 ≤ p, q ≤ ∞. We obtain the equivalent conditions for boundedness and com-pactness of Tμ in terms of Berezin transform and averaging functions. our results extend the main results about Toeplitz operators of Seip and Youssfi (J Geom Anal 23:170–201,2013).

報告人：廣州大學  王曉峰  教授

題目二：A priori estimate for water waves problem with surface tension in a corner domain

内容簡介：We study the two-dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact point. Moreover, when the contact angle is less than $/pi/6$, no singularity appears in our settings. Using elliptic estimates in corner domains and a geometric approach, we prove an a priori estimate for the water waves problem.

報告人：中山大學  明梅  副教授

題目三：Local well-posedness and blow-up phenomenon for a generalization two component Camassa-Holm system

内容簡介：A new generalized two component Camassa-Holm system is derived via the energy variational approach. This system has two parameter which depend on the energy functional. The initial value problem is investigated. The local well-posedness is obtained when the initial density is away from vacuum. Taking advantage of the method of characteristics and the conservation laws we prove a blow up criteria. According to the blow up criteria, we can prove the finite time blow up result under some suitable condition. Moreover, we give some exact expression of traveling solutions. This is a joint work with Yuhui Chen, Wei Luo and Fang Yu.

報告人：中山大學  黃景熾  講師

時  間：2019年4月27日（周六）上午9：00始

地  點：南海樓224室

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2019年4月26日