Geodesic
Solution blowup for systems of shallow-water equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 2, pp. 264-275

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We consider initial-boundary value problems for systems of shallow-water equations. Using the test-function method proposed by Pokhozhaev and Mitidieri, we study the effects of the boundary values and initial conditions on the occurrence, duration, and rate of blowup of the solutions of these problems. Under natural boundary conditions, we prove the existence of blowup in one- and two-dimensional problems in bounded and unbounded regions with dissipation and dispersion.
Keywords: initial-boundary value problem, finite-time blowup, shallow water approximation. 
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     author = {M. O. Korpusov and E. V. Yushkov},
     title = {Solution blowup for systems of shallow-water equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {264--275},
     publisher = {mathdoc},
     volume = {177},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a4/}
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M. O. Korpusov; E. V. Yushkov. Solution blowup for systems of shallow-water equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 2, pp. 264-275. http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a4/