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LiviuIeH)RqetatangAMI(eHthnseitiuaononPHP,uoIpgrrgneebr201embe,Novaris
Liviu Ignat
Paris, November 2010 Joint work with Enrique Zuazua
Institute of Mathematics of the Romanian Academy
Null controllability of the heat equation on the Heinsenberg group
73/10
etuqH)aeontntaoiiuIgLivIMARnat(s,riveNoIHupPaP,rebnorggeHehesni
3
Heat Equation
4
Controlability
5
Carleman inequality
1
Heisenberg Group
/273
Outline
2
Sum of squares vector fields
bmre0201
HeR)eqattiuaononHehtsnieebnerggriLivIungtaI(AM
Heisenberg Group
1
Carleman inequality
5
Controlability
4
Heat Equation
3
2
N,vorasiPHP,uoIp7
Outline
Sum of squares vector fields
03/3r201emberoupreGgesbnHie
= (x1+y1, . . . , x2d+y2d, s+u+12dX(xkyd+kyd+kyk). k=1
(x1, . . . , x2d, s)(y1, . . . , y2d, u)
04/37
or
The Heisenbergh groupHdcan be viewed asR2d+1endowed with the group multiplication
uorGpisenbergHeC×d,RviuI).Liz0)2=(z0s1+,0+sz(z+0s=)0,(z),s(zawplourgehthtiwdewodneember201aris,NovuoIpPHP,neebgrrgeHthnseitiuaononeH)RqetatangAMI(