7 papers
Integer quadratic obstructions to the local controllability of the Burgers equation
Thomas Perrin
We consider the Burgers equation with a scalar control acting through a fixed spatial profile, in a regime where the linearized system is not controllable. We identify natural cond…
Fractional quadratic obstructions to the local controllability of the Burgers equation
Thomas Perrin
We study the local controllability near zero of the Burgers equation with a scalar control and a fixed space-dependent source profile, in the case where the linearized system fails…
Blow-up, decay, and convergence to equilibrium for focusing damped cubic Klein-Gordon and Duffing equations
Thomas Perrin
We study long-time dynamics of the damped focusing cubic Klein-Gordon equation on a compact three-dimensional Riemannian manifold, together with its space-independent reduction, th…
Uniform estimates for solutions of nonlinear focusing damped wave equations
Thomas Perrin
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is boun…
Local controllability around a regular solution and null-controllability of scattering solutions for semilinear wave equations
Thomas Perrin
On a Riemannian manifold with or without boundary, and whether bounded or unbounded, we consider a semilinear wave (or Klein-Gordon) equation with a subcritical nonlinearity (eithe…
Change of regularity in controllability and observability of systems of wave equations
Thomas Perrin
Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary obser…
The damped focusing cubic wave equation on a bounded domain
Thomas Perrin
For the focusing cubic wave equation on a compact Riemannian manifold of dimension , the dichotomy between global existence and blow-up for solutions starting below the energy o…