On the "blow-up'' of solutions of nonlinear wave equations of Sobolev type with cubic sourcesстатья
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Дата последнего поиска статьи во внешних источниках: 16 июня 2015 г.
Местоположение издательства:Road Town, United Kingdom
Первая страница:518
Последняя страница:536
Аннотация:We consider model three-dimensional nonlinear wave equations of Sobolev type with cubic sources, in particular, model three-dimensional equations of Benjamin-Bona-Mahony and Rosenau types with model cubic sources. We also consider an essentially three-dimensional nonlinear equation of spin waves with a cubic source. For these equations, we consider the first initial-boundary value problem in a bounded domain with a smooth boundary. We prove the local solvability in the strong generalized sense and, for an equation of Benjamin-Bona-Mahony type with a source, we prove the unique solvability of the `weakened' solution. We obtain sufficient conditions for the `blow-up' of the solutions of the problems considered. 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 `overturning' of a `weakened' solution in finite time