Internal null controllability of a linear Schrödinger–KdV system on a bounded interval
| Autor: | Alberto Mercado, Mauricio C. Santos, F. D. Araruna, Eduardo Cerpa |
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| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Applied Mathematics 010102 general mathematics Null (mathematics) Mathematical analysis 02 engineering and technology Interval (mathematics) 01 natural sciences Schrödinger equation Dispersionless equation Controllability symbols.namesake 020901 industrial engineering & automation Bounded function symbols Observability 0101 mathematics Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Analysis Mathematics |
| Zdroj: | JOURNAL OF DIFFERENTIAL EQUATIONS Artículos CONICYT CONICYT Chile instacron:CONICYT |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2015.09.009 |
| Popis: | The control of a linear dispersive system coupling a Schrodinger and a linear Korteweg–de Vries equation is studied in this paper. The system can be viewed as three coupled real-valued equations by taking real and imaginary parts in the Schrodinger equation. The internal null controllability is proven by using either one complex-valued control on the Schrodinger equation or two real-valued controls, one on each equation. Notice that the single Schrodinger equation is not known to be controllable with a real-valued control. The standard duality method is used to reduce the controllability property to an observability inequality, which is obtained by means of a Carleman estimates approach. |
| Databáze: | OpenAIRE |
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