Differential and Integral Equations

Quantitative uniqueness for time-periodic heat equation with potential and its applications

K.-D. Phung and G. Wang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Differential Integral Equations, Volume 19, Number 6 (2006), 627-668.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93B05: Controllability
Secondary: 35B10: Periodic solutions 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 35K20: Initial-boundary value problems for second-order parabolic equations 93C20: Systems governed by partial differential equations


Phung, K.-D.; Wang, G. Quantitative uniqueness for time-periodic heat equation with potential and its applications. Differential Integral Equations 19 (2006), no. 6, 627--668. https://projecteuclid.org/euclid.die/1356050356

Export citation