报告人：王丽娟（武汉大学）

邀请人：黄山林

报告题目：A uniform bound on costs of controlling semilinear heat equations on a sequence of increasing domains and its application

报告时间：2020年12月10日（星期四）14：00-16：00

报告地点：科技楼南楼602会议室

报告摘要：In this work, we first prove a uniform upper bound on costs of null controls for semilinear heat equations with globally Lipschitz nonlinearity on a sequence of increasing domains, where the controls are acted on an equidistributed set that spreads out in $\mathbb R^N$. As an application, we then show the exactly null controllability for this semilinear heat equation in the whole Euclidean space $\mathbb R^N$. The main novelty here is that the upper bound on costs of null controls for such kind of equations in large but bounded domains can be made uniformly with respect to the sizes of domains under consideration. The latter is crucial when one uses a suitable approximation argument to derive the global null controllability for the semilinear heat equation in $\mathbb R^N$. This allows us to overcome the well-known problem of the lack of compactness embedding arising in the study of null controllability for nonlinear PDEs in generally unbounded domains.

报告人简介：王丽娟, 武汉大学教授，博士生导师。承担完成国家自然科学基金项目多项。曾在国际顶尖控制论杂志《SIAM J. Control Optim.》发表多篇论文。