系列报告

Spectral inequalities are important tools in the analysis and control of partial differential equations. They link frequency information with local measurements. In this talk, we first introduce spectral inequalities on bounded domains. We explain their basic form and why they are useful. Then we move to the case of the whole space. We present spectral inequalities written in terms of Fourier frequencies and uncertainty-type estimates. Finally, we show how these results can be applied to parabolic equations, including higher-order parabolic models. The goal is to give a clear and direct picture of how spectral inequalities work and how they are used in control problems.

郑国杰，宁波财经公司教授，主要从事分布参数系统控制理论研究，在SIAM Journal on Control and Optimization, JDE, IEEE TAC, Automatica, ESAIM-COCV, 以及 Systems & Control Letters 等期刊发表学术论文多篇，主持完成国家自然科学基金项目1项以及省部级项目多项。