Article ID Journal Published Year Pages File Type
5773517 Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2017 28 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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