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Semilinear parabolic equations of normal type: dynamical properties and nonlocal feedback stbilizationтезисы доклада Электронная публикация
- Автор: Fursikov F.V.
- Сборник: Presetations: http://icms.org.uk/workshops/dynamical
- Тезисы
- Год издания: 2011
- Место издания: Edinburgh (Great Britain)
- Первая страница: 8
- Аннотация: Energy estimate determines many important properties for wide class of equations of Mathematical Physics. For instance, energy estimate for 3D Navier-Stokes system implies existence of generalized solutions, and absence of analogous estimate in phase space $H^1$ for this system is very serious obstacle for solution of millenium problem. By definition of normal type parabolic equation, the nonlinear operator $B$ from this equation satisfies the property: $B(v)$ is collinear to $v$ for each vector $v$. In other words equations of normal type does not satisfy energy estimate in the greatest degree. For some simplest parabolic equations of normal type their dynamical properties including the structure of their phase flow will be described. Construction of nonlocal stabilization by feedback impulse control localised in arbitrary small space subdomain will be given.
- Добавил в систему: Фурсиков Андрей Владимирович