A TIME REVERSAL BASED ALGORITHM FOR SOLVING INITIAL DATA INVERSE PROBLEMS

作者：Ito Kazufumi^*; Ramdani Karim; Tucsnak Marius

来源：Discrete and Continuous Dynamical Systems - Series S, 2011, 4(3): 641-652.

DOI：10.3934/dcdss.2011.4.641

• Time reversal
• initial data inverse problems
• exact observability
• wave equation
• Schrodinger equation

We propose an iterative algorithm to solve initial data inverse problems for a class of linear evolution equations, including the wave, the plate, the Schrodinger and the Maxwell equations in a bounded domain Omega. We assume that the only available information is a distributed observation (i.e. partial observation of the solution on a sub-domain ! during a finite time interval (0; T)). Under some quite natural assumptions (essentially : the exact observability of the system for some time T-obs > 0, T >= T-obs and the existence of a time-reversal operator for the problem), an iterative algorithm based on a Neumann series expansion is proposed. Numerical examples are presented to show the efficiency of the method.

• 出版日期2011-6
• 单位INRIA