In this paper, we consider the homogeneous one-dimensional wave equation defined on (0,π). For every subset ωâŠ[0,π] of positive measure, every T≥2π, and all initial data, there exists a unique control of minimal norm in ...

We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity ...

This paper analyzes the convergence of optimal control problems for an evolution equation in a finite time-horizon [0, T] toward the limit steady state ones as T ?8. We focus on linear problems. We first consider linear ...

We analyze the use of measures of the minimal norm to control elliptic and parabolic equations. We prove the sparsity of the optimal control. In the parabolic case, we prove that the solution of the optimization problem ...

We present some recent results on control and stabilization of waves on 1-d networks.The fine time-evolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a ...

We analyze 1 - d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t→ ∞ of the corresponding solutions of the scalar evolutionary hyperbolic conservation ...

In this paper, we consider the homogeneous one-dimensional wave equation on [0,π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0,π]. Let L∈(0,1). We investigate the problem of maximizing ...

In this paper, we study a nonlinear heat equation with a periodic time oscillating term in factor of the nonlinearity. In particular, we give examples showing how the behavior of the solution can drastically change according ...