{"title":"On Linear Homogeneous Biwave Equations","authors":"Yaqian Bai","doi":"10.4208/jpde.v37.n1.4","DOIUrl":null,"url":null,"abstract":". The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the L ∞ ( R n ) − W N ,1 ( R n ) and L ∞ ( R n ) − W N ,2 ( R n ) estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jpde.v37.n1.4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the L ∞ ( R n ) − W N ,1 ( R n ) and L ∞ ( R n ) − W N ,2 ( R n ) estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations
.双波映射是一类四阶双曲方程。本文主要研究线性均质双波方程的求解公式。根据求解公式和加权能量估计，我们可以分别得到 L ∞ ( R n ) - W N ,1 ( R n ) 和 L ∞ ( R n ) - W N ,2 ( R n ) 估计值。根据我们的结果，我们发现双波图与标准波方程相比具有一些不同的性质
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