Null controllability for the parabolic equation with a complex principal part

2008/05/25 by Fu, Xiaoyu · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.0805.3808

Abstract

This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators (\a+i\b)\pa_t+∑_j,k=1ⁿ\pa_k(a^jk\pa_j) (with real functions \a and \b), by which we develop a universal approach, based on global Carleman estimate, to deduce not only the desired explicit observability estimate for the linearized complex Ginzburg-Landau equation, but also all the known controllability/observability results for the parabolic, hyperbolic, Schrödinger and plate equations that are derived via Carleman estimates.

Cited by

• Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control

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