3 papers
math.OC2026
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…
math.OC2026
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…
math.AP2025
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…