Geodesic
Cauchy problem for waves on shallow water
Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 474-478

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A classical one-dimensional model of shallow water in the class of continuously differentiable functions is considered. A criterion is obtained for the existence of a solution to the Cauchy problem that is global in time. For the special class of step-type initial data, the asymptotic behavior of the solution as $t\to+\infty$ is calculated. 
@article{TMF_1991_86_3_a15,
     author = {R. F. Bikbaev},
     title = {Cauchy problem for waves on shallow water},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {474--478},
     publisher = {mathdoc},
     volume = {86},
     number = {3},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a15/}
}
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R. F. Bikbaev. Cauchy problem for waves on shallow water. Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 474-478. http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a15/