报告人：张登 研究员，上海交通大学
报告题目：随机非线性薛定谔方程系列报告 1
Optimal bilinear control of stochastic nonlinear Schrödinger equations driven by linear multiplicative noise
时间：12月01（周六），上午 9:00-10:00 10：30-11：30
地点：管理科研楼1308
报告摘要： In this talk we consider the optimal bilinear control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrödinger equation with linear multiplicative noise. The existence of an open loop optimal control and first order Lagrange optimality conditions are derived, via Skorohod's representation theorem, Ekeland's variational principle and the existence for the linearized dual backward stochastic equation. The approach in particular applies to the deterministic case. This is a joint work with Viorel Barbu and Michael Röckner.
报告题目：随机非线性薛定谔方程系列报告 2
Scattering for stochastic nonlinear Schrödinger equations
时间：12月01（周六），下午 2:00-3:00 3：30-4：30
地点：管理科研楼1308
报告摘要：
In this talk I will present our recent work on scattering for stochastic nonlinear Schrödinger equations with linear multiplicative noise. In the defocusing case with appropriate range of energy-(sub)critical exponents of nonlinearity, we obtain that the stochastic solutions scatter at infinity in the pseudo-conformal space and in the energy space respectively, under suitable conditions of noises. Moreover, by inputting a large non-conservative noise, we show that the solutions scatter at infinity with high probability for the full energy-subcritical exponents, which indicates the regularization effect of noise on scattering. This is a joint work with Sebastian Herr and Michael Röckner.
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