Structure of dynamical flowow and nonlocal feedback stabilization for normal parabolic equations connected with Helmholtz and Burgers equationsтезисы докладаЭлектронная публикация
Дата последнего поиска статьи во внешних источниках: 11 апреля 2017 г.
Место издания:Immanuel Kant Baltic Federal University Kaliningrad, http://aimg.kantiana.ru/workshop/index.html
Первая страница:9
Аннотация:To understand better properties of equations of Navier-Stokes type we
introduce and study normal parabolic equations (NPE) i.e. semilinear equations
whose nonlinear term B satisfies the condition: for each v belonging to H1 B(v)
is collinear to v.
For 3D Helmholtz equations we derive normal parabolic equations (NPE),
which nonlinear term B(v) is orthogonal projection of nonlinear terms for
Helmholts system on the ray generated by v. Just this term is cause of the
main dificulties arising in construction of smooth solutions for 3D Navier-
Stokes equations. The structure of dynamical flow corresponding to indicated
NPE will be described.
For NPE corresponding to the differentiated 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 to Burgers equations.