|
ИСТИНА |
Войти в систему Регистрация |
ИПМех РАН |
||
Structure of dynamical flow and nonlocal feedback stabilization or normal parabolic equationsтезисы доклада
- Автор: Фурсиков А.В.
- Сборник: Спектральная теория и дифференциальные уравнения. Конференция, посвященная 100-летию Б.М.Левитана. Москва, 23-27 июня 2014 г
- Том: 1
- Тезисы
- Год издания: 2014
- Место издания: Москва
- Первая страница: 10
- Последняя страница: 11
- Аннотация: We introduce and study so-called normal parabolic equations in order to understand better properties of equations of Navier–Stokes type. Semilinear parabolic equation is called normal parabolic equation (NPE) if its nonlinear term B satisfies the condition: for each vector-function v vector-function B(v) is collinear to v. This condition means that solutions of NPE does not satisfies energy estimate “in the most degree”. For 3D Helmholtz equations we derive normal parabolic equations (NPE), which nonlinear term B(v)is orthogonal projection in L2 of nonlinear terms for Helmgoltz equation on the line generated by v. NPE corresponding to Burgers equation is obtained similarly. The structure of dynamical flow corresponding to these NPEs will be discribed. For NPE corresponding to Burgers equation we construct nonlocal feedback stabilization to zero of solutions by starting or impulse controls supported in an arbitrary fixed subdomain of the spatial domain. The last result can be applied to stabilization of solutions for Burgers equations.
- Добавил в систему: Фурсиков Андрей Владимирович