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math.AP2023
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…
math.AP2023
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…
math.AP2023
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…