Control and Stabilization of the Benjamin-Ono Equation in $${L^2({\mathbb{T})}}$$ L 2 ( T )
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| 001 | 605515840 | ||
| 003 | CHVBK | ||
| 005 | 20210128100711.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0887-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0887-5 | ||
| 245 | 0 | 0 | |a Control and Stabilization of the Benjamin-Ono Equation in $${L^2({\mathbb{T})}}$$ L 2 ( T ) |h [Elektronische Daten] |c [Camille Laurent, Felipe Linares, Lionel Rosier] |
| 520 | 3 | |a We study the control and stabilization of the Benjamin-Ono equation in $${L^2(\mathbb{T})}$$ L 2 ( T ) , the lowest regularity where the initial value problem is well-posed. This problem was already initiated in Linares and Rosier (Trans Am Math Soc 367:4595-4626, 2015) where a stronger stabilization term was used (that makes the equation of parabolic type in the control zone). Here we employ a more natural stabilization term related to the L 2-norm. Moreover, by proving a theorem of controllability in L 2, we manage to prove the global controllability in large time. Our analysis relies strongly on the bilinear estimates proved in Molinet and Pilod (Anal PDE 5:365-395, 2012) and some new extension of these estimates established here. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Laurent |D Camille |u Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Boite courrier 187, 75252, Paris Cedex 05, France |4 aut | |
| 700 | 1 | |a Linares |D Felipe |u Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil |4 aut | |
| 700 | 1 | |a Rosier |D Lionel |u Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272, Paris Cedex 06, France |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1531-1575 |x 0003-9527 |q 218:3<1531 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0887-5 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0887-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Laurent |D Camille |u Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Boite courrier 187, 75252, Paris Cedex 05, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Linares |D Felipe |u Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Rosier |D Lionel |u Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272, Paris Cedex 06, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1531-1575 |x 0003-9527 |q 218:3<1531 |1 2015 |2 218 |o 205 | ||