5 papers · 1 filter
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…