Regularization Methods And Comparisons For Ill-posed Abstract Final Value Problems With Nonhomogeneous Terms

There is a lot of inverse problems in natural science, social science and engineering applications. For the observation value which is often obtained by measuring or calcu-lated, will have certain error, so we must consider the stability of solution. The unstable inverse problem is ill-posed, needing regularization processing.The regularization for ill-posed abstract final value problem (or "abstract Cauchy problem") with homogeneous terms has got the system development, and has formed a complete theoretical system since the f960s. But the researches in nonhomogeneous terms are rarely saw. The existing work for nonhomogeneous terms is mostly based on heat conduction problem itself. And the ideal deal to with it is from the ideological homogeneous regularization theory.This paper mainly discusses the parabolic case in nonhomogeneous ill-posed Cauchy problems in Hilbert space. First, the paper gives the abstract representations of the exact solution and the regularized solution, which is to abstract preciously existing work. Secondly, through calculating the errors of regularized solutions and exact solutions are given, we can get the comparisons of the regularization effect. Finally, according to the specific problem, this paper presents numerical experiments. Furthermore the regularized solutions in this paper is helpful to explore new regularization methods.The main conclusions are that: in theory, we can get the fourth method is better than the first method which is better than the third method. And it has also been well illustrated in the numerical experiments. In addition, for specific numerical experiments, we also take the second method to compare respectively with the fourth method and the regularization method in Ames97, getting the second method is better than others. Moreover it is also verified in the numerical experiments.