Geodesic
Blowup of solutions of the~three-dimensional Rosenau--Burgers equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 342-349

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We consider the initial boundary value problem for the well-known three-dimensional Rosenau–Burgers equation in the cylinder $(0,L)\otimes\mathbb{S}$ (where $\mathbb{S}\subset\mathbb{R}^2$) for some boundary conditions. Using the test-function method, we obtain the result on the blowup of solutions of this initial boundary value problem during a finite time. This is one of the first results in the “blowup” direction for this equation.
Keywords: finite-time blowup, Sobolev-type nonlinear equation, nonlinear mixed boundary value problem, hydrodynamics, semiconductor
Mots-clés : Rosenau–Burgers equation. 
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     author = {M. O. Korpusov},
     title = {Blowup of solutions of the~three-dimensional {Rosenau--Burgers} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {342--349},
     publisher = {mathdoc},
     volume = {170},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a2/}
}
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M. O. Korpusov. Blowup of solutions of the~three-dimensional Rosenau--Burgers equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 342-349. http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a2/