确定高阶抛物方程组Cauchy问题的低阶项系数的反问题

Inverse Problem of Determing of Coefficients of Lower Terms of Cauchy Problem for Higher Order Parabolic System

本文讨论常系数高阶抛物方程组Cauchy问题(1.5),(2.5)(或(1.6),(2.7)),在附加条件(2.6)(或(2.18),(2.19))下确定低阶项的一个(或两个),不依赖于变量x_n的未知系数的反问题,证明了问题解的存在、唯一和相依性。

In this paper, under additional conditions (2.6) or (2.18) and (2.19), we consider the inverse problem of determination of one or two coefficients, which are independent of variable x_k, of Cauchy problem (1.5), (2.5) or (1.6), (2.17) for constant coefficient higher order parabolic system. We have proved the problem has an unique solution that is dependent continuously on data.