报告人:刘智慧(香港理工大学)

报告时间: 2017年11月4日(星期六)下午4点---5点30分

报告地点:数统学院203会议室

报告题目: Wong–Zakai-Galerkin Approximations of Stochastic Allen-Cahn Equation

摘要:

We establish an unconditional and optimal strong convergence rate of Wong–Zakai-Galerkin approximations for a stochastic Allen-Cahn type equation driven by an additive Brownian sheet. The key ingredient in the analysis is the fully use of the monotonicity to derive a priori Lq -estimation with sufficiently large q for the solution of this equation, in combination with the factorization method and stochastic calculus in martingale type 2 Banach spaces. These estimations are also used to derive the optimal Sobolev and H¨older regularity with sharp exponents for the solution, which is performed to verify the optimality of the convergence rate of the proposed Wong–Zakai-Galerkin approximations.

报告人简介:

现为香港理工大学博士后，在中国科学院数学与系统科学研究院计算数学与科学⼯程计算研究所获得博士学位。主要研究兴趣为随机偏微分⽅程的适定性理论（解的存在唯⼀性和对初值的连续依赖性）以及最优（Hölder和Sobolev）正则性。随机偏微分⽅程解的密度存在性和正则性（严格正性，光滑性）。随机偏微分⽅程解的遍历性（Feller性和不可约性）。半线性⾮Lipchitz型随机偏微分⽅程的强弱逼近（Galerkin型全离散）最优误差估计(包含随机⾮线性Schrödinger⽅程，随机Navier-Stokes⽅程，随机Burgers⽅程，随机Ginzburg-Landau⽅程。随机相场模型（随机Allen-Cahn⽅程和随机Cahn-Hilliard⽅程以及它们的耦合）适定性、正则性、密度性质、遍历性、强弱逼近。