Inverse coefficient problem for Grushin-type parabolic operators

The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators studied in this paper. Indeed, such estimates are still missing for parabolic operators degenerating in the interior of the space domain. Nevertheless, we are able to prove Lipschitz stability results for inverse coefficient problems for such operators, with locally distributed measurements in arbitrary space dimension. For this purpose, we follow a strategy that combines Fourier decomposition and Carleman inequalities for certain heat equations with nonsmooth coefficients (solved by the Fourier modes)

Boundary controllability for a degenerate wave equation in non divergence form with drift

We consider a degenerate wave equation with drift in presence of a leading operator which is not in divergence form. We provide some conditions for the boundary controllability of the associated Cauchy problem.Comment: 25 page

Null controllability of a population dynamics with interior degeneracy

In this paper, we deal with the null controllability of a population dynamics model with an interior degenerate diffusion. To this end, we proved first a new Carleman estimate for the full adjoint system and afterwards we deduce a suitable observability inequality which will be needed to establish the existence of a control acting on a subset of the space which lead the population to extinction in a finite time

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 will 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 it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established.Comment: Accepted in J. Anal. Math. arXiv admin note: text overlap with arXiv:1508.0401

Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations

We show Carleman estimates, observability inequalities and null controllability results for parabolic equations with non smooth coefficients degenerating at an interior point.Comment: Accepted in Memoirs of the American Mathematical Societ

Interior degenerate/singular parabolic equations in nondivergence form: well-posedness and Carleman estimates

We consider non smooth general degenerate/singular parabolic equations in non divergence form with degeneracy and singularity occurring in the interior of the spatial domain, in presence of Dirichlet or Neumann boundary conditions. In particular, we consider well posedness of the problem and then we prove Carleman estimates for the associated adjoint problem.Comment: Accepted in Journal of Differential Equations. arXiv admin note: text overlap with arXiv:1507.0778

Stability for degenerate wave equations with drift under simultaneous degenerate damping

In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second problem we consider a system that couples degenerate and non-degenerate wave equations, connected through transmission, and subject to a single dissipation law at the boundary of the non-degenerate equation. In both scenarios, we derive exponential stability results