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数学学科现代分析及其应用研究所学术报告(冯斌华 西北师范大学)

发布者:付慧娟   发布时间:2019-11-22  浏览次数:211

报告题目:On the blow-up solutions for the fractional nonlinear Schr?dinger equation with combined power-type nonlinearities

报 告 人:冯斌华 西北师范大学云亭教授



摘要:In this talk, we firstly prove the existence of blow-up solutions and find the sharp threshold mass of blow-up and global existence for the nonlinear Schr?dinger equation with a mass-critical nonlinearity. This is a complement to the result of T. Tao et al. (Comm. Partial Differential Equations 32: 1281-1343, 2007). Secondly, we obtain some sufficient conditions about existence of blow-up solutions for the fractional nonlinear Schr?dinger equation with combined power-type nonlinearities, and then derive some sharp thresholds of blow-up and global existence by constructing some new estimates. Moreover, we find the sharp threshold mass of blow-up and global existence in the mass-critical case. Finally, we investigate the dynamical properties of blow-up solutions, including mass-concentration, blow-up rate and limiting profile.

个人概况:冯斌华,西北师范大学云亭教授,兰州大学博士。研究方向为偏微分方程与数学物理,主要研究玻色-爱因斯坦凝聚中的偏微分方程。已在SIAM J. Control Optim.、J.Differential Equations、J. Dynam. Differential Equations、J. Evolution Equations、Discrete Contin. Dyn. Syst.等专业权威杂志上发表SCI论文30余篇,其中其中ESI高被引论文5篇,目前主持国家自然科学基金青年基金1项。作为主要成员获得甘肃省自然科学一等奖一次。 


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