中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: Prof.Zhi-Qiang Wang（Utah State University, USA）
Inviter: 张志涛
Language: Chinese
Title：Bifurcation solutions of a class of nonlinear elliptic systems
Time&Venue：2026年5月14日（星期四）9:00-10:00 & 南楼N818
Abstract: We discuss recent work on analyzing global structure of solutions in terms of coupling effects for coupled nonlinear elliptic equations, by establishing bifurcation solutions emanating from both signed solutions and nodal solutions. We obtain separated global solution branches by using nodal invariants along connected sets of solutions, and our results reveal complex behavior of solution branches in both attractive and repulsive regimes.
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Speaker: 缑天祥（西安交通大学）
Inviter: 张志涛
Language: Chinese
Title：Nonlinear bound states with prescribed angular momentum in the mass supercritical regime
Time&Venue：2026年5月14日（星期四）10:00-11:00 & 南楼N818
Abstract:This talk concerns the existence, orbital stability/instability and regularity of bound state solutions to nonlinear Schrodinger equations with super-quadratic confinement in two and three spatial dimensions for the mass supercritical case. Such solutions, which are given by time-dependent rotations of a non-radially symmetric spatial profile, correspond to critical points of the underlying energy function subject to the double constraints consisting of the mass and the angular momentum. The study exhibits new pictures for rotating Bose-Einstein condensates within the framework of Gross-Pitaevskii theory. It is proved that there exist two non-radially symmetric solutions, one of which is local minimizer and the other is mountain pass type critical point of the underlying energy function restricted on the constraints. Moreover, we derive that local minimizers are regular, the set of those is orbitally stable and mountain pass type solutions are strongly unstable.
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Speaker: 马琳洁（郑州大学）
Inviter: 张志涛
Language: Chinese
Title：Optimal estimates for the insulated conductivity problem in any dimensions
Time&Venue：2026年5月14日（星期四）11:00-12:00 & 南楼N818
Abstract: In the insulated conductivity problem, the electric (or stress) field can exhibit significant amplification in narrow regions between closely spaced inclusions, with gradients potentially blowing up as the inter-inclusion distance vanishes. In this work, we establish sharp pointwise estimates for solutions with general convex inclusions in arbitrary dimensions. We first derive gradient bounds under the relaxed C1,γ boundary regularity, improving upon the C2,γ assumption in Dong–Li–Yang (2021). We then extend the analysis to obtain higher-order derivative estimates. These results provide new insights into the singular behavior induced by microstructures and represent a notable advancement in understanding the insulated conductivity problem.
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