学 术 报 告
报告题目： On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions
报告时间：2022年4月2日（周六） 上午 9：00-11：30
报告地点：腾讯会议 会议号: 260210118
主讲专家：范恩贵 教授/博导 复旦大学
报告摘要：Abstract. We study the long time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation.Our main technical tool is the representation of the Cauchy problem with an associated matrix Riemann-Hilbert (RH) problem and the consequent asymptotic analysis of this RH problem. Based on the spectral analysis of the Lax pair associated with the mCH equation and scattering matrix, the solution of the Cauchy problem is characterized via the solution of a RH problem in the new scale (y,t). Further using the ∂ generalization of the Deift-Zhou steepest descent method, we derive different long time asymptotic expansions of the solution u(y,t) in different space-time solitonic regions of ξ = y/t. We divide the half-plane {(y,t) : −∞ <y< ∞, t > 0} into four asymptotic regions: The phase function θ(z) has no stationary phase point on the jump contour in the space-time solitonic regions ξ ∈ (−∞, −1/4) ∪ (2, +∞), corresponding asymptotic.
专家介绍：范恩贵，男，复旦大学数学科学学院教授，博士生导师。1999年于大连理工大学获博士学位并进入复旦大学博士后流动站工作，师从谷超豪院士。主要从事可积系统，正交多项式和随机矩阵方面的研究工作，在SIAM J. Math. Anal.，Phys. Rev. E，J. Differ. Equs.等重要期刊发表论文100余篇，被SCI刊源他引3000余次。先后主持和参与多项国家自然科学基金面上项目、重点项目。曾获教育部自然科学二等奖，上海市自然科学二等奖，上海市曙光学者称号，谷超豪数学奖。