Null Controllability for a Degenerate Population Equation with Memory

Null Controllability Results for Degenerate Parabolic Equations

The null controllability of parabolic operators in bounded domains, with both boundary or locally distributed controls, is a well-established property, see, e.g., (Bensoussan et al., 1993) and (Fattorini, 1998). Such a property brakes down, however, for degenerate parabolic operators even when degeneracy occurs on ”small” subsets of the space domain, such as subsets of the boundary. This talk w...

Null controllability for a parabolic equation with nonlocal nonlinearities

In this paper, we establish a local null controllability result for a nonlinear parabolic PDE with nonlocal nonlinearities. The result relies on the (global) null controllability of similar linear equations and a fixed point argument. We also analyze other similar controllability problems and we present several open questions. © 2011 Elsevier B.V. All rights reserved.

Null Controllability of a Nonlinear Heat Equation

Unique continuation and approximate controllability for a degenerate parabolic equation

This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their conormal derivative, are identically equal to zero. An approximate controllability result for weakly degenerate parabolic equations under Dirichlet boundary c...

Internal null-controllability for a structurally damped beam equation

In this paper we study the null-controllability of a beam equation with hinged ends and structural damping, the damping depending on a positive parameter. We prove that this system is exactly null controllable in arbitrarily small time. This result is proven using a combination of Inghamtype inequalities, adapted for complex frequencies, and exponential decay on various frequency bands. We then...