发展型反问题-控制泛函的可微性与收敛性研究

Developmentalinverse problem-study on differentiability and convergence of control functional

考虑从最终实测数据推算线性抛物问题中源项的问题.证明了可以通过伴随抛物问题的解得出控制泛函的Fréchet导数,导出了梯度的Lipschitz连续性,并且得到所考虑反问题的拟解一个存在性结果.最后构造一个基于梯度法的单调迭代格式并证明收敛速度.

The problem of determining the source term in the linear parabolic equation from the measured final data is formulated.It is proved that the Fréchet derivative of the cost functional can be formulated via the solution of the adjoint parabolic problem.The Lipschitz continuity of the gradient is derived,and an existence result for the quasi-solution of the inverse problem is worked out.Finally,a monotone iteration scheme based on gradient method is constructed and the convergence rate is proved.