The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability

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• 作者：Paulo Amorim^a ; ^{paulo@im.ufrj.br} ; Wladimir Neves^a ; José ; Francisco Rodrigues^b
• 关键词：primary ; 35L65 ; secondary ; 35R35
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2017
• 出版时间：January-February 2017
• 年：2017
• 卷：34
• 期：1
• 页码：221-248
• 全文大小：442 K
• 卷排序：34

文摘

In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint introduces a nonlocal Lagrange multiplier in the penalized equation, giving rise to a nonlocal parabolic problem. We introduce a compatibility condition relating the initial datum and the obstacle function which ensures global in time existence of solution. This is not a smoothness condition, but relates to the propagation of the support of the initial datum.