Geodesic
Long Time Asymptotics of Periodic Generalized Entropy Solutions of Scalar Conservation Laws
Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 133-143

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We prove that the periodic generalized entropy solution of a one-dimensional conservation law converges in time to a traveling wave. In this case, the flow function is linear on the minimal interval containing the essential image of the traveling wave profile and the wave velocity coincides with the angular coefficient of the flow function bounded on this interval.
Keywords: conservation law, generalized entropy solution, stabilization property, traveling wave, measure-valued function, compensated compactness. 
@article{MZM_2016_100_1_a9,
     author = {E. Yu. Panov},
     title = {Long {Time} {Asymptotics} of {Periodic} {Generalized} {Entropy} {Solutions} of {Scalar} {Conservation} {Laws}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {133--143},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a9/}
}
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E. Yu. Panov. Long Time Asymptotics of Periodic Generalized Entropy Solutions of Scalar Conservation Laws. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a9/