Geodesic
Periodic solutions of the~Hopf equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 2, pp. 222-230

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We consider the long-time dynamics of approximate solutions of the boundary-value problem for the Hopf equation on a finite segment. Together with the initial conditions, for instance, we impose the zero Dirichlet conditions on both ends of the segment. In this case, all features of solutions associated with the intersections of characteristics are accumulated on a strip bounded by the vertical characteristics emitted from the boundary points.
Keywords: generalized solution, conservation law, Galerkin method. 
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     author = {A. B. Shabat},
     title = {Periodic solutions of {the~Hopf} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {222--230},
     publisher = {mathdoc},
     volume = {177},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a1/}
}
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A. B. Shabat. Periodic solutions of the~Hopf equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 2, pp. 222-230. http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a1/