Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the solution is globally Lipschitz. We then study the large time average of the solution and deduce the asymptotic growth rate of the crystal. Some large time behavior results of the solution are obtained.
{"title":"Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals","authors":"Hiroyoshi Mitake, Hung V. Tran","doi":"10.1112/blms.13227","DOIUrl":"https://doi.org/10.1112/blms.13227","url":null,"abstract":"<p>Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the solution is globally Lipschitz. We then study the large time average of the solution and deduce the asymptotic growth rate of the crystal. Some large time behavior results of the solution are obtained.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 3","pages":"748-770"},"PeriodicalIF":0.8,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13227","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143582073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}