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Аннотация:Parabolic Equation of Normal Type
Connected with 3D Helmholtz System
and Its Nonlocal Stabilization
Andrei Fursikov1;*, 1 Lomonosov Moscow State University,
Voronezh State University, Russia, *fursikov@gmail.com
Abstract
The talk will be devoted to the normal parabolic equation (NPE) con-
nected with 3D Helmholtz system whose nonlinear term B(v) is orthogonal
projection of nonlinear term for Helmholtz system on the ray generated
by vector v. Interest to NPE arised in connection with attempts to find
approaches to solve problem on non local existence of smooth solution for
3D Navier-Stokes equations.
As it became clear now the studies of NPE has been opened the way
to construct the method of nonlocal stabilization by feedback control for
3D Helmholtz as well as for 3D Navier-Stokes equations.
First we describe the structure of dynamical
ow corresponding to
this NPE (see [1]). After, the non local stabilization problem for NPE by
starting control supported on arbitrary fixed subdomain will be formu-
lated. The main steps of solution to this problem will be discussed (see
[2]). At last how to apply this result for solution of nonlocal stabilization
problem with impulse control for 3D Helmholtz system will be explained.
References
[1] Fursikov A. V. \On the Normal-type Parabolic System Corresponding to the
three-dimensional Helmholtz System," Advances in Mathematical Analysis
of PDEs. AMS Transl.Series 2, 232, 99{118 (2014).
[2] Fursikov A. V., Shatina L. S. \Nonlocal stabilization of the normal equa-
tion connected with Helmholtz system by starting control," -ArXiv:
1609.08679v2[math.OC] 26 Feb. 2017, 1-55
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