2024/03/29 by Fabio Ancona, Ancona, Fabio, Luca Talamini +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2404.00116
openalex publication_date 2024/03/29 · openalex created_date 2024/04/03 · openalex updated_date 2026/07/28
Consider a scalar conservation law with a spatially discontinuous flux at a single point x=0, and assume that the flux is uniformly convex when x≠ 0. Given an interface connection (A,B), we define a backward solution operator consistent with the concept of AB-entropy solution [4,13,16]. We then analyze the family A[AB](T) of profiles that can be attained at time T>0 by AB-entropy solutions with L^∞-initial data. We provide a characterization of A[AB](T) as fixed points of the backward-forward solution operator. As an intermediate step we establish a full characterization of A[AB](T) in terms of unilateral constraints and Ole\vınik-type estimates, valid for all connections. Building on such a characterization we derive uniform BV bounds on the flux of AB-entropy solutions, which in turn yield the L1loc-Lipschitz continuity in time of these solutions.