学术通告

Campus news

您现在所在的位置: 首页  学术通告

【预告】钩深讲坛:SINGULARITY FORMATION AND SOLITARY WAVES TO THE SHALLOW WATER MODELING WITH CUBIC NONLINEARITY

更新时间:2020-01-06, 作者:, 浏览人数:16

讲座题目SINGULARITY FORMATION AND SOLITARY WAVES TO THE SHALLOW WATER MODELING WITH CUBIC NONLINEARITY

讲座时间202016(星期一)16:30

讲座地点:数统学院会议室

主 讲 人:刘跃 教授

主讲内容:

In the present study several integrable equations with cubic nonlinearity are derived as asymptotic models from the classical shallow water theory. The starting point in our derivation is the Euler equation for an incompressible fluid with the simplest bottom and surface conditions. The approximate model equations are generated by introducing suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order combining with the Kodama transformation. The so obtained equations can be related to the following integrable systems: the Novikov equation, the modified Camassa-Holm equation, and the Camassa-Holm type equation with cubic nonlinearity. These model equations have a formal bi-Hamiltonian structure and possess single and muti-peaked solutions. Their solutions corresponding to physically relevant initial perturbations are more accurate on a much longer time scale. The effect of the nonlocal higher nonlinearities on wave-breaking phenomena to these quasi-linear model equations are also investigated. Our analysis is approached by applying the method of characteristics and conserved quantities to the Riccati-type differential inequality.

主讲人简介

    刘跃,美国德克萨斯大学阿灵顿分校教授,1994年博士毕业于美国布朗大学,主要从事非线性水波模型问题的研究,在偏微分方程,应用分析和流体力学,一大类浅水波模型的推导、分析、稳定性理论、奇异性形成、局部和整体适定性等方面做出了许多国际一流的工作。其研究成果发表在《Comm. Pure Appl. Math.》《Adv. Math.》《Comm. Math. Phys.》《Arch. Ration.Mech. Anal.》《J. Funct. Anal.》等国际著名刊物上。


友情链接 Link

关于我们  |   联系我们  |   友情链接  |   长师地图  |   宣传资料  |   长师微博  |   滴水崖论坛
中国·重庆·涪陵 地址: 重庆市涪陵区聚贤大道16号 邮编:408100 版权所有©长江师范学院 2013-2015
渝icp备11006140号