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Null controllability of a parabolic system with a cubic coupling term
We consider a system of two parabolic equations with a forcing term present
in one equation and a cubic coupling term in the other one. We prove that the
system is locally null controllable.Comment: 24 page
An obstruction to small time local null controllability for a viscous Burgers' equation
In this work, we are interested in the small time local null controllability
for the viscous Burgers' equation on the line
segment , with null boundary conditions. The second-hand side is a
scalar control playing a role similar to that of a pressure. In this setting,
the classical Lie bracket necessary condition introduced by
Sussmann fails to conclude. However, using a quadratic expansion of our system,
we exhibit a second order obstruction to small time local null controllability.
This obstruction holds although the information propagation speed is infinite
for the Burgers equation. Our obstruction involves the weak norm of
the control . The proof requires the careful derivation of an integral
kernel operator and the estimation of residues by means of weakly singular
integral operator estimates
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