相关论文: Sharp estimates of the one-dimensional boundary co…

The general goal of this work is to obtain upper and lower bounds for the $L^2$-norm of biorthogonal families to complex exponential functions associated to sequences $\{ \Lambda_k \}_{k \ge 1} \subset \mathbb C$ which satisfy appropriate…

We consider the one-dimensional degenerate parabolic equation $$ u_t - (x^\alpha u_x)_x =0 \qquad x\in(0,1),\ t \in (0,T) ,$$ controlled by a boundary force acting at the degeneracy point $x=0$. First we study the reachable targets at some…

In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties.…

In this paper we study the local boundary controllability for a non linear system of two degenerate parabolic equations with a control acting on only one equation. We analyze boundary null controllability properties for the linear system…

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for…

In this article we study the minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems when all the controls are acting on the same side of the boundary. We establish an explicit and easy-to-compute…

We consider the typical one-dimensional strongly degenerate parabolic operator $Pu= u_t - (x^\alpha u_x)_x$ with $0<x<\ell$ and $\alpha\in(0,2)$, controlled either by a boundary control acting at $x=\ell$, or by a locally distributed…

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a…

In this paper we introduce a method to find the minimal control time for the null controllability of 1D first-order linear hyperbolic systems by one-sided boundary controls when the coefficients are regular enough.

In this paper, we consider the following degenerate/singular parabolic equation $$ u_t -(x^\alpha u_{x})_x - \frac{\mu}{x^{2-\alpha}} u =0, \qquad x\in (0,1), \ t \in (0,T), $$ where $0\leq \alpha <1$ and $\mu\leq (1-\alpha)^2/4$ are two…

This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the…

We derive sharp bounds for the boundary control cost of the one-dimensional fractional Schr\"odinger and heat equations. The analysis of the lower bound is based on the study of the control cost of a related singular boundary control…

In this paper, we prove the null controllability of a one-dimensional fourth-order degenerate parabolic equation with a singular potential. Here, we analyze cases where boundary control conditions are applied at the left endpoint. We…

We prove the null controllability of a one dimensional degenerate parabolic equation with drift and a singular potential. We study the case the potential arises at the left end point and the weighted Dirichlet boundary control is located at…

This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control…

In this paper we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular…

We are concerned about the controllability of a general linear hyperbolic system of the form $\partial_t w (t, x) = \Sigma(x) \partial_x w (t, x) + \gamma C(x) w(t, x) $ ($\gamma \in \mR$) in one space dimension using boundary controls on…

In this paper we prove a uniform controllability result for a fourth order parabolic partial differential equation which includes a transport term, when the coefficients of higher order terms vanish. We prove the null controllability of the…

The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…

In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the desired evolution profile together with the cost of a control.…