Journal of Inverse and Ill-Posed Problems

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

Nguyen Van Duc 1
, 
Nguyen Van Thang 2
, 
Pham Quy Muoi 3
1
 
2
 
Quan Hanh Secondary School , Quan Hanh Town , Nghi Loc District, Nghe An Province , Vietnam
3
 
Department of Mathematics , The University of Danang – University of Science and Education , 459 Ton Duc Thang , Danang , Vietnam
Publication type: Journal Article
Publication date: 2025-02-11
scimago Q2
SJR: 0.546
CiteScore: 2.6
Impact factor: 0.9
ISSN: 09280219, 15693945
Abstract

In this paper, we study the Kuramoto–Sivashinsky (KS) equation backward in time. First, we prove a stability estimate of Hölder type. Then the ill-posed problem is regularized by the Tikhonov regularization method, and an error estimate of Hölder type is obtained. Finally, we apply a physics-informed neural network method to solve the problem numerically.

Found 
  • We do not take into account publications without a DOI.
  • Statistics recalculated only for publications connected to researchers, organizations and labs registered on the platform.
  • Statistics recalculated weekly.

Are you a researcher?

Create a profile to get free access to personal recommendations for colleagues and new articles.
Share
Cite this
GOST | RIS | BibTex
Found error?