Modified Quasi Boundary Value method for inverse source biparabolic
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 th...
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doaj-1e0ab9c6b13a4bd7b5ddc2de77c14fb62020-12-02T08:48:16ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482020-07-0143113214210.31197/atnaa.752335Modified Quasi Boundary Value method for inverse source biparabolicNguyen Duc PhuongNguyen Hoang LucLe Dinh LongIn 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. https://dergipark.org.tr/tr/download/article-file/1212311fractional diffusion equationinverse probleminverse source problemregularization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nguyen Duc Phuong Nguyen Hoang Luc Le Dinh Long |
spellingShingle |
Nguyen Duc Phuong Nguyen Hoang Luc Le Dinh Long Modified Quasi Boundary Value method for inverse source biparabolic Advances in the Theory of Nonlinear Analysis and its Applications fractional diffusion equation inverse problem inverse source problem regularization |
author_facet |
Nguyen Duc Phuong Nguyen Hoang Luc Le Dinh Long |
author_sort |
Nguyen Duc Phuong |
title |
Modified Quasi Boundary Value method for inverse source biparabolic |
title_short |
Modified Quasi Boundary Value method for inverse source biparabolic |
title_full |
Modified Quasi Boundary Value method for inverse source biparabolic |
title_fullStr |
Modified Quasi Boundary Value method for inverse source biparabolic |
title_full_unstemmed |
Modified Quasi Boundary Value method for inverse source biparabolic |
title_sort |
modified quasi boundary value method for inverse source biparabolic |
publisher |
ATNAA |
series |
Advances in the Theory of Nonlinear Analysis and its Applications |
issn |
2587-2648 2587-2648 |
publishDate |
2020-07-01 |
description |
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.
|
topic |
fractional diffusion equation inverse problem inverse source problem regularization |
url |
https://dergipark.org.tr/tr/download/article-file/1212311 |
work_keys_str_mv |
AT nguyenducphuong modifiedquasiboundaryvaluemethodforinversesourcebiparabolic AT nguyenhoangluc modifiedquasiboundaryvaluemethodforinversesourcebiparabolic AT ledinhlong modifiedquasiboundaryvaluemethodforinversesourcebiparabolic |
_version_ |
1724407635737837568 |