Genni Fragnelli

Null controllability of degenerate parabolic operators with drift

We give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain. For this purpose, we obtain an observability inequality for the adjoint problem using suitable Carleman estimates.

Carleman estimates and observability inequalities for parabolic equations with interior degeneracy

Abstract. We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on Carleman estimates for the associated adjoint problem. The novelty of interior degeneracy does not let us adapt previous Carleman estimates to our situation. As an application, observability inequalities are established.

Carleman estimates for singular parabolic equations with interior degeneracy and non-smooth coefficients

Abstract We establish Carleman estimates for singular/degenerate parabolic Dirichlet problems with degeneracy and singularity occurring in the interior of the spatial domain. Our results are completely new, since this situation is not covered by previous contributions for degeneracy and singularity on the boundary. In addition, we consider non-smooth coefficients, thus preventing the use of standard calculations in this framework.

Stability of Solutions for Some Classes of Nonlinear Damped Wave Equations

We consider two classes of semilinear wave equations with nonnegative damping which may be of type “on-off” or integrally positive. In both cases we give a sufficient condition for the asymptotic stability of the solutions. In the case of integrally positive damping we show that such a condition is also necessary.

Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that, for the first time, the problem is considered as one with an interior degeneracy and Neumann boundary conditions, so no previous result can be adapted to this situation. As a consequence, new observability inequalities are established.

Identification of a diffusion coefficient in strongly degenerate parabolic equations with interior degeneracy

We are concerned with the identification of the diffusion coefficient u(x) in a strongly degenerate parabolic diffusion equation. The strong degeneracy means that

A k-uniform Maximum Principle When 0 is an Eigenvalue

{u \in W^{1,\infty}}

The Brezis–Oswald Result for Quasilinear Robin Problems

u∈W1,∞, u vanishes at an interior point of the space domain and