Abstract: For the inverse problem respect to parameter inversion of two dimensional parabobic equation with variable coefficients，the paper transforms the inverse problem to the optimized problem of operator theory，this approach can evolve the optimal coefficient estimation by the Quasi-Newton mthod in the giving function space of unknown parameter from observation data objectively and automaticall.The approach is successfully put into practice to solve the inverse problem of two_dimensional parabobic equation whose coefficient is partition paragraph function.The numerical results demonstrate the effectiveness of this method.

Key words: parabobic equation, inverse problem, the Quasi-Newton method

摘要： 讨论了二维变系数抛物型方程的参数识别反问题，将其归为最优化问题，指定待定参数的函数类形式，用拟牛顿法来演化待求参数的最优估计值，并将该方法运用于线性扩散方程和具有分段函数系数的二维抛物型方程的参数识别反问题的数值模拟中，数值结果表明拟牛顿法（BFGS）解决此类问题是有效的和可行的。

关键词: 抛物型, 反问题, 拟牛顿法