Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866909231948496896 |
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| author | Filho, Roberto de A. Capistrano Tanaka, Thiago Yukio |
| author_facet | Filho, Roberto de A. Capistrano Tanaka, Thiago Yukio |
| contents | The main goal of this manuscript is to prove the existence of insensitizing controls for the fourth-order dispersive nonlinear Schrödinger equation with cubic nonlinearity. To obtain the main result we prove a null controllability property for a coupled fourth-order Schrödinger cascade type system with zero-order coupling which is equivalent to the insensitizing control problem. Precisely, employing a new Carleman estimate, we first obtain a null controllability result for the linearized system around zero, and then the null controllability for the nonlinear case is extended using an inverse mapping theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_15104 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion Filho, Roberto de A. Capistrano Tanaka, Thiago Yukio Analysis of PDEs 35Q55, 93C20, 93B05, 93B07, 93C41 The main goal of this manuscript is to prove the existence of insensitizing controls for the fourth-order dispersive nonlinear Schrödinger equation with cubic nonlinearity. To obtain the main result we prove a null controllability property for a coupled fourth-order Schrödinger cascade type system with zero-order coupling which is equivalent to the insensitizing control problem. Precisely, employing a new Carleman estimate, we first obtain a null controllability result for the linearized system around zero, and then the null controllability for the nonlinear case is extended using an inverse mapping theorem. |
| title | Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion |
| topic | Analysis of PDEs 35Q55, 93C20, 93B05, 93B07, 93C41 |
| url | https://arxiv.org/abs/2010.15104 |