有限元方法在一维和二维抛物方程参数辨识中的应用

THE FINITE ELEMENT METHOD APPLIED TO THE PARAMETER IDENTIFICATION OF PARABOLIC EQUATIONS

§1.引言 本文考虑分布参数系统 ? 在Ω×[0,T]中的参数辨识问题,即通过u的某种观测确定参数a,f及u_0.但一般预先知道u_0和f,因而本文仅考虑参数a的辨识问题.(1)中的Ω是R^n中的有界区域,?Ω为其边界.

Convergence is proved for one and two dimensional distributed parameter identificationproblems by the finite element method and optimization techniques. The result is valid notonly for distributed observations, but also for point observations.