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Dergiler / Advances in the Theory of Nonlinear Analysis and its Application / 2026 / Cilt: 4 Sayı: 3

Modified Quasi Boundary Value method for inverse source biparabolic

Nguyen Duc Phuong(Industrial University of Ho Chi Minh City)0000-0003-3779-197X
Nguyen Luc(Thu Dau Mot University)0000-0001-9664-6743
Le Dinh Long(Thu Dau Mot University)0000-0001-8805-4588
Sayfa
132–142
Yayın Tarihi
2020-08-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, we present the estimation between the regularized solution and the sought solution by using a priori regularization parameter choice rule.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we study an inverse source problem of the bi-parabolic equation.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:In addition, we present the estimation between the regularized solution and the sought solution by using a priori regularization parameter choice rule.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Inverse source biparabolic · Ill-posed problem · Regularization

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.

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Bu Makaleye Atıf Yap

Phuong, N. D., Luc, N., Long, L. D. (2020). Modified Quasi Boundary Value method for inverse source biparabolic. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 4 Sayı: 3, 132–142. https://doi.org/10.31197/atnaa.752335

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