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2006 Quantitative uniqueness for time-periodic heat equation with potential and its applications
K.-D. Phung, G. Wang
Differential Integral Equations 19(6): 627-668 (2006).

Abstract

In this paper, we establish a quantitative unique continuation property for some time-periodic linear parabolic equations in a bounded domain $\Omega$. We prove that for a time-periodic heat equation with particular time-periodic potential, its solution $u(x,t)$ satisfies $\left\| u(\cdot,0) \right\| _{L^{2}(\Omega) }\leq C\left\| u(\cdot,0) \right\| _{L^{2}(\omega) }$ where $\omega\subset\Omega$. Also we deduce the asymptotic controllability for the heat equation with an even, time-periodic potential. Moreover, the controller belongs to a finite dimensional subspace and is explicitly computed.

Citation

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K.-D. Phung. G. Wang. "Quantitative uniqueness for time-periodic heat equation with potential and its applications." Differential Integral Equations 19 (6) 627 - 668, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.93025
MathSciNet: MR2234717

Subjects:
Primary: 93B05
Secondary: 35B10 , 35B60 , 35K20 , 93C20

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 6 • 2006
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