Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773517 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 28 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Paulo Amorim, Wladimir Neves, José Francisco Rodrigues,