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Normal Equation Generated from Helmholtz System: Nonlocal Stabilization by Starting Control and Properties of Stabilized Solutions

  • A. V. Fursikov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 273)

Abstract

We consider the semilinear normal parabolic equation (NPE) corresponding to the 3D Helmholtz system with periodic boundary conditions. First, we recall the main definitions and results associated with the NPE including a result on stabilization to zero of the solution for NPE with arbitrary initial condition by starting control. The main content of the paper is to study properties of stabilized solution of NPE.

Keywords

Semilinear normal parabolic equation 3D Helmholtz system Stabilisation theory Navier-Stokes equations 

Notes

Acknowledgments

The work has been fulfilled by RAS program “Theoretical problems of modern mathematics", project “Optimization of numerical algorithms of Mathematical Physics problems". The author was supported in part by RFBI Grants 15-01-03576 and 15-01-08023.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and Mathematics“Lomonosov” Moscow State UniversityMoscowRussian Federation

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