Regularization Method For A Class Of Wave Source Identification Problem

The problems of determining unknown non-homogeneous term of PDE are also called the problems of identification unknown source. This kind of problem has a wide range of applications, such as which heat conduction equation of the unknown source identification is usually applied to the determination of groundwater pollution sources, environmental protection and energy diffusion source to determine; unknown source of identification of the wave equation currently makes application for the geophysical exploration. Therefore, such a problem has caused widespread concern by many scholars.In this thesis, we study the problems of identification wave source, and consider the following one-dimensional wave equation:where f(x)∈L2(x). In order to determine the unknown source of the wave equation studied in this thesis, we need an additional data. The additional data in this thesis, observations at a final moment t=1, is given as follows: u(x,1)=g(x),0≤x≤1.By using simplified Tikhonov regularization method, the inverse problem is reduced to an operator equation; a regularization solution is obtained and error estimate of regularization solution is given. In the last, this problem is verified by using the numerical simulation. The numerical result showed that simplified Tikhonovregularization method is effective and the wave source function can be well figuredout.