一类扩散控制系统的数值识别与参数反演

NUMERICAL IDENTIFICATION AND PARAMETERS INVERSION FOR SOME DIFFUSION CONTROL SYSTEMS

考虑在化学工业中具有应用模型的一类反应扩散控制系统．此类系统带有两个未知参数，一个是未知扩散系数D=D（x）；另一个是反应控制参数k（k为常数参数，例如：k为反应速度）．采用有限元数值方法，给出函数参数D(x)的有限元逼近解，将其极小化问题的有限元逼近解作为新的常数控制扩散参数，利用所给部分信息数据或可观测数据（它们是非完全信息数据），确定系统的另一未知参数k．

This Paper is concerned with some reaction-diffusion control systems withapplied models in chemical industry. There are two unknown parameters in this kind of systems.One of the parameters is the diffusion coefficient D = D(x), and the other one is the reactioncontrol parameter k (k is a constaflt parameter, e.g. k is the reaction rate). A numericalapprokimation to the function parameter D(x) is given by the finite element method. Aftertaking the minimizer approximation solution to the minimization problem as a new constancontrol parameter, the other parameter k of the system can be determined by the given or themeasu-red data (which is a partial information data).