Geodesic
On the ``Destruction'' of Solutions of Nonlinear Wave Equations of Sobolev Type with Cubic Sources
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 559-578

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We consider model three-dimensional wave nonlinear equations of Sobolev type with cubic sources, and foremost, model three-dimensional equations of Benjamin–Bona–Mahony and Rosenau types with model cubic sources. An essentially three-dimensional nonlinear equation of spin waves with cubic source is also studied. For these equations, we investigate the first initial boundary-value problem in a bounded domain with smooth boundary. We prove local solvability in the strong generalized sense and, for an equation of Benjamin–Bona–Mahony type with source, we prove the unique solvability of a “weakened” solution. We obtain sufficient conditions for the “destruction” of the solutions of the problems under consideration. These conditions have the sense of a “large” value of the initial perturbation in the norms of certain Banach spaces. Finally, for an equation of Benjamin–Bona–Mahony type, we prove the “failure” of a “weakened” solution in finite time. 
@article{MZM_2005_78_4_a6,
     author = {M. O. Korpusov and A. G. Sveshnikov},
     title = {On the {``Destruction''} of {Solutions} of {Nonlinear} {Wave} {Equations} of {Sobolev} {Type} with {Cubic} {Sources}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {559--578},
     publisher = {mathdoc},
     volume = {78},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a6/}
}
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M. O. Korpusov; A. G. Sveshnikov. On the ``Destruction'' of Solutions of Nonlinear Wave Equations of Sobolev Type with Cubic Sources. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 559-578. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a6/