相关论文: Null controllability of a degenerate parabolic equ…

This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous…

In this paper, we focus on two types of degenerate partial differential equations: a degenerate elliptic equation and a degenerate parabolic equation. Significantly, both categories are characterized by the same principal operator. To…

We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $\Omega = \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the…

The main objective of this paper is to establish the null controllability for the fourth order semilinear parabolic equations with the nonlinearities involving the state and its gradient up to second order. First of all, based on optimal…

In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one…

This paper is devoted to the partial null controllability issue of parabolic linear systems with n equations. Given a bounded domain in R N, we study the effect of m localized controls in a nonempty open subset only controlling p components…

This paper examines the impulse controllability of degenerate singular parabolic equations through a modern framework focused on finite-time stabilization. Furthermore, we provide an explicit estimate for the exponential decay of the…

We establish Carleman estimates for singular/degenerate parabolic Dirichlet problems with degeneracy and singularity occurring in the interior of the spatial domain. Our results are completely new, since this situation is not covered by…

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a semilinear parabolic equation in one-dimension defined in a non-cylindrical domain where the diffusion coefficient degenerates at one point of the…

This work studies the null controllability of a system of coupled parabolic PDEs. In particular, our work specializes to an important subclass of these control problems which are coupled by first and zero-order couplings and are,…

We consider a degenerate wave equation with drift in presence of a leading operator which is not in divergence form. We provide some conditions for the boundary controllability of the associated Cauchy problem.

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

We consider the linear degenerate wave equation, on the interval $(0, 1)$ $$ w_{tt} - (x^\alpha w_x)_x = p(t) \mu (x) w, $$ with bilinear control $p$ and Neumann boundary conditions. We study the controllability of this nonlinear control…

We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.

This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…

We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.

We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is…

In this article, we study the uniform null controllability problem for a system of coupled parabolic equations with an oscillating coefficient. This is done in three steps -- first, we study the spectral properties of an elliptic operator;…

This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators…

This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…