一类重构非线性抛物型方程系数的反问题

An Inverse Problem of Reconstructing the Coefficient in A Nonlinear Parabolic Equation

研究了一个利用附加条件反演非线性抛物型方程未知系数的反问题.基于最优控制理论,证明了控制泛函极小元满足的必要条件以及局部唯一性与稳定性.在反问题的计算中,运用Gradient型迭代法进行数值模拟.数值结果表明该算法是稳定的,而且未知系数反演的效果也很好.

An inverse problem is investigated by using the additional conditions to reconstruct the unknown coefficient of the nonlinear parabolic equation.Based on the optimal control framework,the necessary condition which must be satisfied by the minimize is deduced,and the local uniqueness and stability of the solution are proved.In the process of computation of the inverse problem,the numerical simulation with the Gradient iterative method is conducted.The numerical results show that the algorithm designed in this paper is stable and that the unknown coefficient is recovered very well.