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.

引用

页数：14

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