学术报告-梁歌春

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2018-07-19 15:55:00

学术报告

题      目:A Hopf-Lax splitting approximation for semilinear parabolic PDEs with convex and coercive Hamiltonians

报  告  人:梁歌春   教授  (邀请人:杨舟)

                          华威大学


时      间:2018-07-19 16:00--17:00

地      点:学院401

报告人简介:

       梁歌春,英国华威大学(University of Warwick)统计系副教授。之前任职于伦敦国王大学和牛津大学。2011年博士毕业于牛津大学。研究方向为随机控制和金融数学。研究工作发表于Annals of Probability,Finance and Stochastics 和 SIAM Journal on Control and Optimization 等期刊。


摘      要:

       We propose a new approximation scheme to solve a class of semilinear parabolic equations that are convex and coercive in their gradients. By splitting the original equation into a linear parabolic equation and a Hamilton-Jacobi equation, we are able to solve both equations explicitly. In particular, we solve the associated Hamilton-Jacobi equation by the Hopf-Lax formula. We prove that the solution of the approximation scheme converges to the viscosity solution of the equation. We also obtain its convergence rate using Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation.