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Structure of dynamical flow and nonlocal feedback stabilization for normal parabolic equationsтезисы доклада
- Автор: Fursikov A.V.
- Сборник: The Seventh International Conference on Differential and Functional Differential Equations, Moscow, Russia, August 22–29, 2014. Book of abstracts
- Тезисы
- Год издания: 2014
- Место издания: PFUR Moscow, Russia
- Первая страница: 44
- Аннотация: We study parabolic equations of so-called normal type for better understanding properties of equations of Navier–Stokes type. By definition, a semilinear parabolic equation is called normal (NPE) if its non- linear term defined by an operator B satisfies the following condition: for each vector v belonging Sobolev space H1, the vector B(v) is collinear to v. In other words, solutions to NPEs do not satisfy the energy estimate “in the most degree.” For the Burgers and the 3-D Helmholtz equations, we derive NPEs whose nonlinear terms B(v) are orthogonal projections of nonlinear terms of the original equations on the straight line, generated by the vector v. The structure of the dynamical flow correspondent to these NPEs will be described. For the NPE corresponding to the Burgers equation, we construct nonlocal stabilization of solutions to zero by applying starting, impulse, or distributed feedback control supported in an arbitrary fixed subdomain of the spatial domain. The last result is applied to nonlocal stabilization of solutions for the Burgers equation.
- Добавил в систему: Фурсиков Андрей Владимирович