Null controllability of the heat equation on the Heinsenberg group

Zuazua Enrique

Description

Null controllability of the heat equation on the Heinsenberg group Liviu Ignat Institute of Mathematics of the Romanian Academy Paris, November 2010 Joint work with Enrique Zuazua Liviu Ignat (IMAR) Heat equation on the Heinsenberg group IHP, Paris, November 2010 1 / 37

• romanian academy


• liviu ignat


• heinsenberg group


• squares vector


• null controllability


• cd ?


• heat equation

Sujets

• Heisenberg group
• Romanian Academy
• Heat equation
• multiplication

Informations

• Publié par: pefav
• Nombre de lectures: 24
• Langue: English

Extrait

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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

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HeR)eqattiuaononHehtsnieebnerggriLivIungtaI(AM

Heisenberg Group

1

Carleman inequality

5

Controlability

4

Heat Equation

3

2

N,vorasiPHP,uoIp7

Outline

Sum of squares vector fields

03/3r201embe roupreGgesbnHie

= (x 1 +y 1 , . . . , x 2d +y 2d , s+u+ 1 2 d X (x k y d+k −y d+k y k ). k=1

(x 1 , . . . , x 2d , s)◦(y 1 , . . . , y 2d , u)

04/37

or

The Heisenbergh groupH d can be viewed asR 2d+1 endowed with the group multiplication

uorGpisenbergHe C× d ,R viuI ). Li ∙z 0 ) 2 =(z 0 s 1 +, 0 +sz(z+ 0 s=) 0 ,(z)◦,s(z awplourgehthtiwdewodne ember201aris,NovuoIpPHP,neebgrrgeHthnseitiuaononeH)RqetatangAMI(