Research on inverse problems and boundary control problems for partial differential equations having transport and nonlocal terms

点击翻译按钮获取中文摘要

Inverse problems and boundary control problems for partial differential equations having transport and nonlocal terms are investigated by the method of deformation formulas. For the transport diffusion equations, the investigator has determined uniquely the transport term by boundary observaton, and for the associated control system having nonlocal terms, he has constructed a concrete boundary feedback control law which makes the system a desirable stable state. The key to solve the problems is to use the deformation formula which deforms the transport term and nonlocal terms simultaneously, and the investigator has solved the problem of existence and construction of such a deformation kernel function. In addition, the deformation formula is extended to a system of first order Volterra integro-differential equations. By using the kernel, he has solved the related inverse and boundary control problems for the Volterra system.