7 papers
Global null-controllability for stochastic semilinear parabolic equations
Víctor Hernández-Santamaría, Kévin Le Balc'h, Liliana Peralta
In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in t…
Exponential bounds for gradient of solutions to linear elliptic and parabolic equations
Kévin Le Balc'h
In this paper, we prove global gradient estimates for solutions to linear elliptic and parabolic equations. For a sufficiently smooth bounded convex domain ,…
Approximate controllability of the linearized Boussinesq system in a two dimensional channel
Kévin Le Balc'h
In this paper, we prove an approximate controllability result for the linearized Boussinesq system around a fluid at rest, in a two dimensional channel, when the control acts only…
Null-controllability of linear parabolic-transport systems
Karine Beauchard, Armand Koenig, Kévin Le Balc'h
Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find…
Global null-controllability and nonnegative-controllability of slightly superlinear heat equations
Kévin Le Balc'H
We consider the semilinear heat equation posed on a smooth bounded domain of with Dirichlet or Neumann boundary conditions. The control input is a source term…
Local controllability of reaction-diffusion systems around nonnegative stationary states
Kévin Le Balc'H
We consider a nonlinear reaction-diffusion system posed on a smooth bounded domain of . This system models reversible chemical reactions. We act on t…