13 papers
The Allen-Cahn equation with nonlinear truncated Laplacians: description of radial solutions
Matthieu Alfaro, Philippe Jouan
We consider the Allen-Cahn equation with the so-called truncated Laplacians, which are fully nonlinear differential operators that depend on some eigenvalues of the Hessian matrix.…
General Nilpotent and Solvable Approximations of Almost-Riemannian Structures
Yacine Chitour, Philippe Jouan, Ronald Manríquez
It is first shown that the nilpotent or the solvable approximation of an almost-Riemannian structure at a singular point is always a linear almost-Riemannian structure on a Lie gro…
Jordan decomposition and the recurrent set of flows of automorphisms
Victor Ayala, Adriano Da Silva, Philippe Jouan
In this paper we show that any linear vector field on a connected Lie group admits a Jordan decomposition and the recurrent set of the associated ow of automorphi…
Control sets of linear systems on semi-simple Lie groups
Victor Ayala, Adriano Da Silva, Philippe Jouan +1
In this paper we study the main properties of control sets with nonempty interior of linear control systems on semisimple Lie groups. We show that, unlike the solvable case, linear…
Isometries of almost-Riemannian structures on Lie groups
Philippe Jouan, Zsigmond Guilherme, Victor Ayala
A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) -- 1 left-invariant ones. It is first p…
Convergence Rate of Nonlinear Switched Systems
Philippe Jouan, Saïd Naciri
This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of…