2020/08/27 by Misha Perepelitsa, Perepelitsa, Misha
Engineering · Mathematics · #35L60 #35L65 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.2008.12354
openalex publication_date 2020/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a dispersion approximation of weak, entropy solutions of multidimensional scalar conservation laws using variational kinetic representation, where equilibrium densities satisfy the Gibb's entropy minimization principle for a piecewise linear, convex entropy. For such solutions, we show that small scale discontinuities, measured by the entropy increments, propagate with characteristic velocities, while the large scale, shock-type discontinuities propagate with speeds close to the speeds of classical shock waves. In the zero-limit of the scale parameter, approximate solutions converge to a unique, entropy solution of a scalar conservation law.