报告人：张土生（中国科学技术大学）

邀请人：吴付科

报告时间：2022年6月30日 （星期四）16: 00-17:30  

报告地点：科技楼706室

报告题目：Global well-posedness to stochastic reaction-diffusion equations on the real line R with superlinear drifts driven by multiplicative space-time white noise.

报告摘要：When I is a compact interval, say I = [0,1], the well-posedness of the above equation was established in [DKZ] (Ann. Prob. 47:1,2019). The case where I = R was left open. The essential obstacle is calused by the explosion of the supremum norm of the solution,making the usual truncation procedure invalid. In this paper, we prove that there exists a unique global solution to the stochastic reaction-diffusion equation on the whole real line R with logarithmic nonlinearity. Because of the nonlinearity, to get the uniqueness, we are forced to work with the first order moment of the solutions on the space.Our approach depends heavily on the new, precise lower order moment estimates of the stochastic convolution and a new type of Gronwall's inequalities we obtained, which are of interest on their own right.

报告人简介：张土生，中国科学技术大学教授。国际知名的概率论专家，现担任《Stochastic  Processes and Their Applications》，《Journal of Theoretical  Probability》，《Communications in Mathematics and  Statistics》等国际著名刊物的编委。张土生教授的研究领域是随机分析和随机偏微分方程。