# American Institute of Mathematical Sciences

September  2014, 13(5): 1815-1854. doi: 10.3934/cpaa.2014.13.1815

## Stabilization of the simplest normal parabolic equation

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

Received  November 2013 Revised  April 2014 Published  June 2014

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.
Citation: Andrei Fursikov. Stabilization of the simplest normal parabolic equation. Communications on Pure &amp; Applied Analysis, 2014, 13 (5) : 1815-1854. doi: 10.3934/cpaa.2014.13.1815
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