基于一类抛物型方程的反问题

Evolutional Inverse Coefficient Problem by Optimization Method

研究了一类重构的系数同时依赖于时间变量x和空间变量t的反问题,在最优化理论框架下,首先证明了控制泛函的最优解的存在性,其次给出了最优解所要满足的必要条件,最后得到了当网格参数趋于零时最优解的收敛性.

An inverse problem of reconstructing source coefficient is investigated,which depends on both the space variable x and the time variable t.Based on the optimal control framework,the ex-istence of the optimal solution of the cost functional is proved,and the necessary condition which must be satisfied by the optimal solution is given.At last,the convergence of the optimal solution when the mesh parameters tend to zero is also established.