16 citations · 40 across the 9 of their papers we have counts for
13 papers
Optimal control of linear non-local parabolic problems with an integral kernel
Umberto Biccari, Víctor Hernández-Santamaría, Loic Louison +1
We consider a linear non-local heat equation in a bounded domain , , with Dirichlet boundary conditions, where the non-locality is given by the prese…
Controllability of a simplified time-discrete stabilized Kuramoto-Sivashinsky system
Víctor Hernández-Santamaría
In this paper, we study some controllability and observability properties for a coupled system of time-discrete fourth- and second-order parabolic equations. This system can be reg…
Existence and convergence of solutions to fractional pure critical exponent problems
Víctor Hernández-Santamaría, Alberto Saldaña
We study existence and convergence properties of least-energy symmetric solutions (l.e.s.s.) to the pure critical problem \begin{equation*} (-Δ)^su_s=|u_s|^{2^\star_s-2}u_s, \quad…
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…
Local-controllability of the one-dimensional nonlocal Gray-Scott model with moving controls
Víctor Hernández-Santamaría, Kévin Le Balc'h
In this paper, we prove the local-controllability to positive constant trajectories of a nonlinear system of two coupled ODE equations, posed in the one-dimensional spatial setting…
Controllability results for stochastic coupled systems of fourth- and second-order parabolic equations
Víctor Hernández-Santamaría, Liliana Peralta
In this paper, we study some controllability and observability problems for stochastic systems coupling fourth- and second-order parabolic equations. The main goal is to control bo…
Existence and cost of boundary controls for a degenerate/singular parabolic equation
Umberto Biccari, Víctor Hernández-Santamaría, Judith Vancostenoble
In this paper, we consider the following degenerate/singular parabolic equation where …
Local null-controllability of a nonlocal semilinear heat equation
Víctor Hernández-Santamaría, Kévin Le Balc'h
This paper deals with the problem of internal null-controllability of a heat equation posed on a bounded domain with Dirichlet boundary conditions and perturbed by a semilinear non…
Some remarks on the Robust Stackelberg controllability for the heat equation with controls on the boundary
Víctor Hernández-Santamaría, Liliana Peralta
In this paper, we present some controllability results for the heat equation in the framework of hierarchic control. We present a Stackelberg strategy combining the concept of cont…
The Poisson equation from non-local to local
Umberto Biccari, Víctor Hernández-Santamaría
We analyze the limit behavior as of the solution to the fractional Poisson equation , with homogeneous Dirichlet boundary conditions $u_s\equiv 0…
Null controllability of linear and semilinear nonlocal heat equations with integral kernel
Umberto Biccari, Víctor Hernández-Santamaría
We consider a linear nonlocal heat equation in a bounded domain with Dirichlet boundary conditions. The non-locality is given by the presence of an integral…
A Finite Element approximation of the one-dimensional fractional Poisson equation with applications to numerical control
Umberto Biccari, Víctor Hernández-Santamaría
We present a finite element (FE) scheme for the numerical approximation of the solution to a non-local Poisson equation involving the one-dimensional fractional Laplacian $(-d_x^2)…
Robust Stackelberg controllability for a parabolic equation
Víctor Hernández-Santamaría, Luz de Teresa
The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, \textit{the leader}, that is responsible for a null controllability…