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López Montes, Antonio and Zuazua Iriondo, Enrique (1998) Some new results related to the null controllability of the 1d heat equation. Other. École Polytechnique, Palaiseau, Paris.

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Official URL: http://sedp.cedram.org/item?id=SEDP_19971998____A8_0
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Abstract
We address three null controllability problems related to the $1d$ heat equation. First we show that the $1d$ heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finitedifference semidiscretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained as limit of null controllability properties for singularly perturbed dissipative wave equations. The proofs combine results on sums of real exponentials, Carleman’s inequalities for heat equations and sideways energy estimates for wave equations.
Item Type:  Monograph (Other) 

Uncontrolled Keywords:  Controllability; Heat equation; Systems governed by partial differential equations 
Subjects:  Sciences > Physics > Mathematical physics Sciences > Mathematics > Differential equations 
ID Code:  21515 
Deposited On:  23 May 2013 10:54 
Last Modified:  12 Dec 2018 15:08 
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