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# On large time behavior of periodic entropy solutions to scalar conservation laws

Abstract: We prove that a periodic entropy solution to a one-dimensional scalar conservation law converges as time $t\to+\infty$ to a traveling wave. Moreover, the flux function is shown to be affine on the segment $[\alpha,\beta]$ containing the essential range of the traveling wave profile, and the speed of the traveling wave coincides with the slope of the line $v=\varphi(u)$, $u\in [\alpha,\beta]$.

Paper:
Available as PDF (193 Kbytes).
Author(s):
E. Yu. Panov
Submitted by:
; 2015-08-11.