7 papers
Obstacles and Singularities of Riemannian Distance Functions
Paolo Albano, Piermarco Cannarsa, Carlo Sinestrari
We study the distance function from a point target in the complement of a compact obstacle endowed with a smooth Riemannian metric. We prove that the obstacle necessarily generates…
Long-time behavior of generalized gradient flows of solutions to Hamilton-Jacobi equations
Paolo Albano, Piermarco Cannarsa, Wei Cheng +1
We study the long-time behavior of the generalized gradient flow associated with solutions of the critical Hamilton-Jacobi equation for mechanical Hamiltonians on the flat torus. F…
Uniform stabilization for relatively bounded perturbations of generators of semigroup
Shri Lal Raghudev Ram Singh, Piermarco Cannarsa, Roberto Guglielmi
In this paper, we study the robustness of exponential stability for semigroups generated by linear operators under perturbations. Extending a classical result of Gibson's Stability…
Reconstruction of degeneracy region and power for parabolic equations and systems
Piermarco Cannarsa, Veronica Danesi, Anna Doubova
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative…
Comparison principles and long time behavior for a diffusive Energy Balance Model with vertical resolution
Piermarco Cannarsa, Valerio Lucarini, Patrick Martinez +2
We study a two-layer one-dimensional energy balance model, which allows for vertical energy exchanges between a surface layer and the atmosphere, as well as meridional energy trans…
Global propagation of singularities for magnetic mechanical systems
Piermarco Cannarsa, Wei Cheng, Jiahui Hong +1
We prove that singularities propagate globally for viscosity solutions of Hamilton-Jacobi equations related to magnetic mechanical systems on closed Riemannian manifolds. Our main…