Rosier, L.. "Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain ." ESAIM: Control, Optimisation and Calculus of Variations 2 (2010): 33-55. <http://eudml.org/doc/116551>.
@article{Rosier2010,
abstract = {
The exact boundary controllability of linear and nonlinear Korteweg-de
Vries equation on bounded domains with various boundary conditions is
studied. When boundary conditions bear on spatial derivatives up to
order 2, the exact controllability result by Russell-Zhang is directly
proved by means of Hilbert Uniqueness Method. When only the first
spatial derivative at the right endpoint is assumed to be controlled,
a quite different analysis shows that exact controllability holds too.
From this last result we derive the exact boundary controllability for
nonlinear KdV equation on bounded domains, for sufficiently small initial
and final states.
},
author = {Rosier, L.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Korteweg-de Vries equation / boundary controllability /
Hilbert uniqueness method.; controllability; Hilbert uniqueness method; boundary control; nonlinear Korteweg-de Vries equation; bounded domains; fixed point theorem},
language = {eng},
month = {3},
pages = {33-55},
publisher = {EDP Sciences},
title = {Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain },
url = {http://eudml.org/doc/116551},
volume = {2},
year = {2010},
}
TY - JOUR
AU - Rosier, L.
TI - Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 2
SP - 33
EP - 55
AB -
The exact boundary controllability of linear and nonlinear Korteweg-de
Vries equation on bounded domains with various boundary conditions is
studied. When boundary conditions bear on spatial derivatives up to
order 2, the exact controllability result by Russell-Zhang is directly
proved by means of Hilbert Uniqueness Method. When only the first
spatial derivative at the right endpoint is assumed to be controlled,
a quite different analysis shows that exact controllability holds too.
From this last result we derive the exact boundary controllability for
nonlinear KdV equation on bounded domains, for sufficiently small initial
and final states.
LA - eng
KW - Korteweg-de Vries equation / boundary controllability /
Hilbert uniqueness method.; controllability; Hilbert uniqueness method; boundary control; nonlinear Korteweg-de Vries equation; bounded domains; fixed point theorem
UR - http://eudml.org/doc/116551
ER -
