Null controllability for the parabolic equation with a complex principal part

Xiaoyu Fu

Null controllability for the parabolic equation with a complex principal part

Optimization and Control 2008-05-27 v1

Authors: Xiaoyu Fu

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 $(\a+i\b)\pa_t+\sum\limits_{j,k=1}^n\pa_k(a^{jk}\pa_j)$ (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, Schr\"odinger and plate equations that are derived via Carleman estimates.

Keywords

controllability theory carleman estimates parabolic partial differential equations

Cite

@article{arxiv.0805.3808,
  title  = {Null controllability for the parabolic equation with a complex principal part},
  author = {Xiaoyu Fu},
  journal= {arXiv preprint arXiv:0805.3808},
  year   = {2008}
}

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