报告人:米永生 (长江师范学院)

日  期:2019年6月6日

时  间:上午10:40

地  点:理科楼 LA106

摘  要:In this talk, we shall introduce some recent progress on the generalized Camassa-Holm equation (system). First of all, , we consider a higher order shallow water equation, and obtain the local well-posedness of solutions for the Cauchy problem in Sobolev space. Under some assumptions, the existence and uniqueness of the global solutions is establishd. Based some conditions, we also prove the development of singularities in finite time for the solutions and the weak solution for the equation. Secondly, a new model is improved. We also establish the local well-posedness in a range of the Besov spaces and the precise blow-up scenario. Moreover, we prove that peakon solutions to the equation are global weak solutions. Finally, the continuation of solutions to the generalized Camassa-Holm equation beyond wave breaking is considered. A continuous semigroup of global conservative and dissipative solutions are obtained. We show that the solutions are conservative, in the sense that the total energy equals to a constant, for almost every time, while the solutions are dissipative, energy loss occurs through wave breaking.

报告人简介：米永生，男，长江师范学院教授。2004 年7 月毕业于吉林大学获学士学位，2014 年7 月毕业于太阳成集团获理学博士学位，2014 年7 月至2017 年8 月在北京应用物理与计算数学研究所从事博士后研究。2009 年破格晋升讲师，2012 年破格晋升副教授，2014 年破格晋升教授，2016 年入选重庆市“巴渝学者”特聘教授， 2017 年入选“重庆市青年拔尖人才特殊支持计划”， 2018 年获 “重庆市十佳科技青年奖”，2015 年获“重庆市自然科学二等奖”。近年来，主持国家自然科学基金项目2 项（面上、青年），在“Journa of Differential Equations”（ 5篇）、 “Proceedings of the Royal Society of Edinburgh: Section A Mathematics” 等国内外SCI期刊发表论文40余篇。

公司联系人:穆春来

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