相关论文: Carleman estimates and null controllability for a …

Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we tackle the problem of determining the distribution of the population density of a social space…

We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calder\'on's problem. In a previous result by the authors on monotonicity-based reconstruction, the perturbed coefficient is…

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…

In this paper, we investigate Carleman estimate and controllability result for the fully-discrete approximations of a one-dimensional Ginzburg-Landau equation with dynamic boundary conditions. We first establish a new discrete Carleman…

We analyze a class of general nonlinear epidemic models with age and space structure, including a nonlocal infection term depending on age and space. After establishing the well-posedness of the state partial differential equation, we…

In the present paper we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with…

The exact controllability to the origin for linear evolution control equation is considered.The problem is investigated by its transformation to infinite linear moment problem. Conditions for the existence of solution for infinite linear…

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of…

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

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…

We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…

We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…

This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…

This paper aims to establish null controllability for systems coupled by two backward fourth order stochastic parabolic equations. The main goal is to control both equations with only one control act on the drift term. To achieve this, we…

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.

It is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is…

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…

As the aging population grows, particularly for the baby boomer generation, the United States is witnessing a significant increase in the elderly population experiencing multifunctional disabilities. These disabilities, stemming from a…

In this paper, we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy-Neumann problems. First, we will obtain embedding results for weighted Sobolev spaces, that have proved decisive in…

We consider a $2\times 2$ system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse…