Stabilization of the simplest normal parabolic equation

Andrei Fursikov

doi:10.3934/cpaa.2014.13.1815

Article Contents

2014, Volume 13, Issue 5: 1815-1854. Doi: 10.3934/cpaa.2014.13.1815

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Stabilization of the simplest normal parabolic equation

Andrei Fursikov^1,

1.
Department of Mechanics & Mathematics, Moscow State University, Moscow 119991

Received: October 31, 2013

Revised: March 31, 2014

Published: August 2015

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Abstract

The simplest semilinear parabolic equation of normal type with periodic boundary condition is considered, and the problem of stabilization to zero of its solution with arbitrary initial condition by starting control supported in a prescribed subset is investigated. This problem is reduced to one inequality for starting control, and the proof of this inequality is given.

Keywords:

Equations of normal type,
stabilization by starting control.

Mathematics Subject Classification: Primary: 37D10, 40H05; Secondary: 35K57, 35B38.

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