Resolution of the Transport equation subject to constraint
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摘要
We present a method for solving the Transport equation when its solution has to belong to a constrained set which is not required to be convex. An autonomous formulation of the characteristics method allows us to use the tangency condition which has been introduced for ordinary differential equations. Thus we obtain a sufficient condition for existence of solutions, which shows the interplay between the geometry of the constraints set K and the velocity field β. A numerical method is proposed for solving the problem when the sufficient condition is not satisfied. A numerical experiment is presented showing the efficiency of the algorithm proposed.
论文关键词:35F40,35L85,35R05,Characteristic curves,Autonomous system,Set of non-convex constraints,Tangency condition
论文评审过程:Received 28 September 2006, Revised 14 March 2007, Available online 1 May 2007.
论文官网地址:https://doi.org/10.1016/j.cam.2007.04.019