On the long time behavior of almost periodic entropy solutions to scalar\n conservation laws

2017/01/07 by Evgeny Yu. Panov, Panov, Evgeny Yu.
Mathematics · #35B15 #35B40 #35L65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1701.01808

openalex publication_date 2017/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We found the precise condition for the decay as t\→\∞ of Besicovitch\nalmost periodic entropy solutions of multidimensional scalar conservation laws.\nMoreover, in the case of one space variable we establish asymptotic convergence\nof the entropy solution to a traveling wave (in the Besicovitch norm). Besides,\nthe flux function turns out to be affine on the minimal segment containing the\nessential range of the limit profile while the speed of the traveling wave\ncoincides with the slope of the flux function on this segment.\n

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