Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation
Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation
复制标题
时间分数扩散方程源项稀疏结构的时间相关分量的数值解
DOI：
10.1016/j.camwa.2018.11.012
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
Wen Zhang
中科院分区：
文献类型：
--
作者：
Zhousheng Ruan;Sen Zhang;Wen Zhang
本文考虑了时间分数阶扩散方程源项的一个具有稀疏结构的反时变分量。利用拉普拉斯变换技术证明了非局部观测数据反问题的唯一性。考虑到源项的稀疏性，我们将源项反问题转化为一个弹性网络正则化优化问题。采用半光滑牛顿法求解优化问题，并证明了半光滑牛顿法的超收敛性。数值算例验证了算法的有效性。
We consider an inverse time-dependent component of source term with sparse structure for the time fractional diffusion equation in the present paper. We prove the uniqueness of the inverse problem with nonlocal observation data by Laplace transform technique. Concerning the sparsity of the source term, we transform the inverse source problem into an elastic-net regularization optimization problem. The semi-smooth Newton method is adopted to solve the optimization problem and the superconvergence of the semi-smooth Newton algorithm is proven. Several numerical examples are tested to verify the efficiency of the algorithm.