论文标题
关于由PDE建模的反问题
On inverse problems modeled by PDE's
论文作者
论文摘要
我们研究了Maz'ya和Kozlov提出的迭代方法（请参见[3]，[4]），以解决由PDE建模的不良重建问题。我们考虑椭圆，双曲线和抛物线类型的线性时间依赖性问题。分析方法的每次迭代都包括解决良好的边界（或初始）值问题的解决方案。如[4]中，迭代被描述为仿射操作员的能力。我们使用光谱理论和一些功能分析结果为算法提供了替代性收敛证明（参见[5]，[6]）。
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each iteration of the analyzed methods consists on the solution of a well posed boundary (or initial) value problem. The iterations are described as powers of affine operators, as in [4]. We give alternative convergence proofs for the algorithms, using spectral theory and some functional analytical results (see [5], [6]).
