Geodesic
On the velocity of separation between two successive traveling waves in the asymptotics of the solution to the Cauchy problem for a Burgers-type equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 6, pp. 1069-1071 
A. V. Gasnikov. On the velocity of separation between two successive traveling waves in the asymptotics of the solution to the Cauchy problem for a Burgers-type equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 6, pp. 1069-1071. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_6_a11/
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     title = {On the velocity of separation between two successive traveling waves in the asymptotics of the solution to the {Cauchy} problem for a {Burgers-type} equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An upper bound on the distance between the centers of two successive traveling waves occurring in the asymptotics of the solution to the Cauchy problem for a Burgers-type equation is established under generic conditions. Taking into account a previously established lower bound, an asymptotically sharper estimate is derived.

[1] Gasnikov A. V., “O promezhutochnoi asimptotike resheniya zadachi Koshi dlya kvazilineinogo uravneniya parabolicheskogo tipa s monotonnym nachalnym usloviem”, Izv. RAN. Teoriya i sistemy upravleniya, 2008, no. 3, 154–163 | MR | Zbl

[2] Gasnikov A. V., “Asimptoticheskoe po vremeni povedenie resheniya nachalnoi zadachi Koshi dlya zakona sokhraneniya s nelineinoi divergentnoi vyazkostyu”, Izv. RAN. Ser. matem., 76:6 (2009), 39–76 | DOI | MR | Zbl

[3] Gasnikov A. V., “Skhodimost po forme resheniya zadachi Koshi dlya kvazilineinogo uravneniya parabolicheskogo tipa s monotonnym nachalnym usloviem k sisteme voln”, Zh. vychisl. matem. i matem. fiz., 48:8 (2008), 1458–1487 | MR | Zbl

[4] Engelberf S., Schochet S., “Nonintegrable perturbation of scalar viscous shock profiles”, Asymptotic Analysis, 48 (2006), 121–140 | MR

[5] Henkin G. M., “Asymptotic structure for solutions of the Cauchy problem for Burgers type equations”, J. Fixed point theory appl., 1:2 (2007), 239–291 | DOI | MR | Zbl

[6] Henkin G. M., Polterovich V. M., “A difference-differential analogue of the Burgers equation: stability of the two-wave behavior”, J. Nonlinear Sci., 4 (1994), 497–517 | DOI | MR | Zbl

[7] Gasnikov A. V., Klenov S. L., Nurminskii E. A. i dr., Vvedenie v matematicheskoe modelirovanie transportnykh potokov, ed. A. V. Gasnikov, MFTI, M., 2010