{"title":"Backward behavior and determining functionals for chevron pattern equations","authors":"V.K. Kalantarov , H.V. Kalantarova , O. Vantzos","doi":"10.1016/j.cam.2024.116282","DOIUrl":null,"url":null,"abstract":"<div><div>The paper is devoted to the study of the backward behavior of solutions of the initial boundary value problem for the chevron pattern equations under homogeneous Dirichlet’s boundary conditions. We prove that, as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, the asymptotic behavior of solutions of the considered problem is completely determined by the dynamics of a finite set of functionals. Furthermore, we provide numerical evidence for the blow-up of certain solutions of the backward problem in finite time in 1D.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"457 ","pages":"Article 116282"},"PeriodicalIF":2.6000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005314","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/9/18 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is devoted to the study of the backward behavior of solutions of the initial boundary value problem for the chevron pattern equations under homogeneous Dirichlet’s boundary conditions. We prove that, as , the asymptotic behavior of solutions of the considered problem is completely determined by the dynamics of a finite set of functionals. Furthermore, we provide numerical evidence for the blow-up of certain solutions of the backward problem in finite time in 1D.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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