Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science

Global null-controllability and nonnegative-controllability of slightly superlinear heat equations

We consider the semilinear heat equation posed on a smooth bounded domain $Ω$ of $\mathbb{R}^{N}$ with Dirichlet or Neumann boundary conditions. The control input is a source term localized in some arbitrary nonempty open subset $ω$ of $Ω$. The goal of this paper is to prove the uniform large time global null-controllability for semilinearities $f(s) = \pm |s| \log^α(2+|s|)$ where $α\in [3/2,2)$ which is the case left open by Enrique Fernandez-Cara and Enrique Zuazua in 2000. It is worth mentioning that the free solution (without control) can blow-up. First, we establish the small-time global …

趋化系统到非负轨迹的精确能控性

Exact controllability to nonnegative trajectory for a chemotaxis system

本文利用Hopf-Cole变换和新全局Carleman估计，研究具有奇异敏感度的Keller-Segel趋化系统到非负轨迹的精确能控性，并讨论非负解的全局存在性。

Approximate controllability for nonlinear degenerate parabolic problems with bilinear control

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 reaching well-posedness for nonlinear degenerate problems. Then, we show that the above systems can be steered in $L^2$ from any nonzero, nonnegative initial state into any neighborhood of any desirable nonnegative target-state by bilinear piecewise static controls. Moreover, we extend the above result relaxing the sign constraint on the initial date.

Controllability under positivity constraints of multi-d wave equations

We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class of wave equations with time-independent coefficients. According to it, the system can be driven from a steady state generated by a strictly positive control to another, by means of nonnegative controls, when the time of control is long enough. Secondly, under the added assumption of conservation and coercivity of the energy, controllability is proved betwee…

具有局部移动支撑的乘法或非负加性控制下一维热方程的可控性性质

Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support

研究一维热方程在乘法或非负加性控制下的非负近似可控性，建立了静态与移动控制支撑下的可控性结果。

Controllability of a Linear System with Nonnegative Sparse Controls

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system is unidirectional, and activating each input node adds to the cost of control. We derive the necessary and sufficient conditions for controllability of the system, without imposing any constraints on the system matrices. Unlike the well-known Kalman rank based controllability criteria, the conditions presented in this paper can be verified in polynomial time,…