Global BV entropy solutions to the Gauss-Codazzi system

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• 作者：Wentao Cao ^{cwt@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：BV entropy solutions ; Gauss&ndash ; Codazzi system ; System of balance laws ; Metric
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：444
• 期：2
• 页码：1015-1026
• 全文大小：341 K

文摘

The Gauss–Codazzi system for the given metric whose Gauss curvature is negative, is considered in the present paper. We provide some suitable conditions on the given metric such that the system admits a global BV entropy solution. Our main approach is applying the method of seeking global BV entropy solutions to the hyperbolic system of balance laws to the Gauss–Codazzi system. The global existence of BV solutions to the Gauss–Codazzi system yields a C^1,1 isometric immersion of two dimensional manifold into R³.