Control and stabilization of the periodic fifth order Korteweg-de Vries equation

Flores, Cynthia; Smith, Derek L.

doi:10.1051/cocv/2018033

Flores, Cynthia ¹ ; Smith, Derek L.¹

¹

ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 38

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Résumé

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H$$(𝕋), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regularity property, yields a smoothing effect permitting the application of the contraction principle.

MR Zbl

DOI : 10.1051/cocv/2018033

Classification : 35Q53, 93B05, 93D15
Keywords: Korteweg-de Vries equation, periodic domain, propagation of regularity, exact controllability, stabilization

Affiliations des auteurs :

Flores, Cynthia ¹ ; Smith, Derek L. ¹

¹

@article{COCV_2019__25__A38_0,
     author = {Flores, Cynthia and Smith, Derek L.},
     title = {Control and stabilization of the periodic fifth order {Korteweg-de} {Vries} equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2019},
     publisher = {EDP Sciences},
     volume = {25},
     doi = {10.1051/cocv/2018033},
     zbl = {1437.35610},
     mrnumber = {4003462},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2018033/}
}

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Flores, Cynthia; Smith, Derek L. Control and stabilization of the periodic fifth order Korteweg-de Vries equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 38. doi: 10.1051/cocv/2018033

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