Special Session 98: Control, Inverse problems and Long time dynamics of Evolutionary Systems

Null controllability of strongly degenerate parabolic equations
Lionel ROSIER
Universite du Littoral Cote d`Opale
France
Co-Author(s):    Antoine Benoit and Romain Loyer
Abstract:
We consider linear one-dimensional strongly degenerate parabolic equations with measurable coefficients that may be degenerate or singular. Taking 0 as the point where the strong degeneracy occurs, we assume that the coefficients $a=a(x)$ in the principal part of the parabolic equation is such that the function $a->x/a(x)$ is in $L^p(0,1)$ for some $p>1$. After establishing some spectral estimates for the corresponding elliptic problem, we prove that the parabolic equation is null controllable in the energy space by using one boundary control.