Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension
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Bibliographic record
Abstract
In this paper, we consider a parabolic PDE on a torus of arbitrary dimension. The nonlinear term is a smooth function of polynomial growth of any degree. In this general setting, the Cauchy problem is not necessarily well posed. We show that the equation in question is approximately controllable by only a finite number of Fourier modes. This result is proved by using some ideas from the geometric control theory introduced by Agrachev and Sarychev.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
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| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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