- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 3
- Modified Quasi Boundary Value method for inverse source biparabolic
Modified Quasi Boundary Value method for inverse source biparabolic
Authors : Nguyen Duc PHUONG, Nguyen LUC, Le Dinh LONG
Pages : 132-142
Doi:10.31197/atnaa.752335
View : 4 | Download : 2
Publication Date : 2020-08-31
Article Type : Research
Abstract :In this study, we study an inverse source problem of the bi-parabolic equation. The problem is severely non-well-posed in the sense of Hadamard, the problem is called well-posed if it satisfies three conditions, such as the existence, the uniqueness, and the stability of the solution. If one of the these properties is not satisfied, the problem is called is non well-posed (ill-posed). According to our research experience, the stability properties of the sought solution are most often violated. Therefore, a regularization method is required. Here, we apply a Modified Quasi Boundary Method to deal with the inverse source problem. Base on this method, we give a regularized solution and we show that the regularized solution satisfies the conditions of the well-posed problem in the sense of Hadarmad. In addition, we present the estimation between the regularized solution and the sought solution by using a priori regularization parameter choice rule.Keywords : Inverse source biparabolic, Ill-posed problem, Regularization