报告题目：Water-waves problem in corner domains

报告人：明梅

摘要：我将介绍水波问题适定性理论的发展现状尤其是带接触角的水波问题解的局部适定性的发展情况，并且展示我们目前最新的研究成果：带表面张力和两个接触角的二维有界水波问题的解的局部适定性，此时接触角小于pi/2.

报告题目：Numerical approximations of one point large deviations rate functions of non-globally Lipschitz SDEs with small noise

报告人：陈子恒

摘要：This paper investigates the numerical approximations of one point large deviations rate functions of the backward Euler method for non-globally Lipschitz stochastic differential equations (SDEs) with small noise. Our setting allows the underlying drift coefficient to grow super-linearly and thus includes the well-known stochastic Ginzburg--Landau equation and stochastic Verhulst equation as examples. It is shown that the backward Euler method satisfies the one point large deviations principle (LDP) with a numerical rate function. Further, the uniform convergence order of numerical rate function on any given bounded set is obtained based on the equivalent characterizations of rate functions and the continuity of the original rate function. More precisely, the convergence order is 1/2 in the multiplicative case and 1 in the additive case, respectively. Some numerical experiments are finally reported to confirm these theoretical results.

时间：2023年3月8日下午4：00-6：00

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