Approximate Null-Controllability with Uniform Cost for the Hypoelliptic Ornstein–Uhlenbeck Equations

Uniform Schauder Estimates for Regularized Hypoelliptic Equations

In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields: L = ∑m i=1X 2 i + ∆ in Rn, where ∆ is the Laplace operator, m < n, and the limit operator L = ∑m i=1X 2 i is hypoelliptic. Here we establish Schauder’s estimates, uniform with respect to the parameter , of solution of the approximated equation L u = f , using a modification of the lift...

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...

On the null-controllability of diffusion equations

Null Controllability for Parabolic Equations with Dynamic Boundary Conditions

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

Null and approximate controllability for weakly blowing up semilinear heat equations

We consider the semilinear heat equation in a bounded domain of IR, with control on a subdomain and homogeneous Dirichlet boundary conditions. We prove that the system is null-controllable at any time provided a globally defined and bounded trajectory exists and the nonlinear term f(y) is such that |f(s)| grows slower than |s| log(1+|s|) as |s| → ∞. For instance, this condition is fulfilled by ...