Stability estimate and the Tikhonov regularization method for the Kuramoto-Sivashinsky equation backward in time

被引：0
|
作者：
Duc, Nguyen Van [1 ]
Thang, Nguyen Van [2 ]
Muoi, Pham Quy [3 ]
机构：
[1] Vinh Univ, Dept Math, Vinh City, Vietnam
[2] Quan Hanh Secondary Sch, Quan Hanh, Nghe An, Vietnam
[3] Univ Danang, Univ Sci & Educ, Dept Math, 459 Ton Duc Thang, Danang, Vietnam
来源：
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2025年
关键词：
Kuramoto-Sivashinsky equation backward in time; stability estimate; Tikhonov regularization method; LIQUID-FILM; NETWORKS; FLOW; INSTABILITY; BEHAVIOR; SYSTEMS; WAVES;
D O I：
10.1515/jiip-2024-0064
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the Kuramoto-Sivashinsky (KS) equation backward in time. First, we prove a stability estimate of H & ouml;lder type. Then the ill-posed problem is regularized by the Tikhonov regularization method, and an error estimate of H & ouml;lder type is obtained. Finally, we apply a physics-informed neural network method to solve the problem numerically.
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页数：14
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