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

利用变形公式的方法研究了具有传输项和非局部项的偏微分方程组的反问题和边界控制问题。对于输运扩散方程，通过边界观测法唯一地确定了输运项，对于具有非局部项的相关控制系统，构造了使系统达到理想稳定状态的具体边界反馈控制律。解决这些问题的关键是使用同时变形传输项和非局部项的变形公式，而研究者解决了这种变形核函数的存在和构造问题。此外，将变形公式推广到一阶Volterra积分微分方程组。利用核，他解决了Volterra系统的相关逆和边界控制问题。

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.