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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we prove a general result giving the maximum and the antimaximum principles in a unitary way for linear operators of the form , provided that is an eigenvalue of with associated constant eigenfunctions. To this purpose, we introduce a new notion of “quasi”–uniform maximum principle, named –uniform maximum principle: it holds for belonging to certain neighborhoods of depending on the fixed positive multiplier which selects the good class of right-hand-sides. Our approach is based on a estimate for some related problems. As an application, we prove some generalization and new results for elliptic problems and for time periodic parabolic problems under Neumann boundary conditions. [Copyright &y& Elsevier]

Abstract: We consider a system of two degenerate parabolic equations with nonlocal terms and Dirichlet boundary conditions. More precisely, the degeneracy in each equation of the system is of the type -Laplacian where is a function depending on , where Ω is a bounded smooth domain of . The system models the diffusion and the interaction between two different biological species sharing the same territory Ω. The paper provides conditions on the parameters of the problem that guarantee the coexistence of a T-periodic non-negative solution with both non-trivial . [Copyright &y& Elsevier]