On large time behavior of periodic entropy solutions to scalar conservation laws
E. Yu. Panov
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 $v=\varphi(u)$, $u\in [\alpha,\beta]$.