Turnpike in optimal control of PDEs, ResNets, and beyond
B Geshkovski, E Zuazua - Acta Numerica, 2022 - cambridge.org
The turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …
seeks to move an economy from one level of capital to another, then the most efficient path …
Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
Dynamic phenomena in social and biological sciences can often be modeled by reaction-
diffusion equations. When addressing the control from a mathematical viewpoint, one of the …
diffusion equations. When addressing the control from a mathematical viewpoint, one of the …
Controllability of the one-dimensional fractional heat equation under positivity constraints
In this paper, we analyze the controllability properties under positivity constraints on the
control or the state of a one-dimensional heat equation involving the fractional Laplacian …
control or the state of a one-dimensional heat equation involving the fractional Laplacian …
Controllability of the Stefan problem by the flatness approach
We show the boundary controllability to stationary states of the Stefan problem with two
phases and in one dimension in the space variable. In the case of an initial condition that is …
phases and in one dimension in the space variable. In the case of an initial condition that is …
Controllability properties from the exterior under positivity constraints for a 1-d fractional heat equation
We study the controllability to trajectories, under positivity constraints on the control or the
state, of a one-dimensional heat equation involving the fractional Laplace operator …
state, of a one-dimensional heat equation involving the fractional Laplace operator …
Nonnegative boundary control of 1D linear heat equations
J Lohéac - Vietnam Journal of Mathematics, 2021 - Springer
We consider the controllability of a one dimensional heat equation with nonnegative
boundary controls. Despite the controllability in any positive time of this system, the …
boundary controls. Despite the controllability in any positive time of this system, the …
Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states
In this paper we study the global approximate multiplicative controllability for nonlinear
degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional …
degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional …
State-constrained controllability of linear reaction-diffusion systems
We study the controllability of a coupled system of linear parabolic equations, with
nonnegativity constraint on the state. We establish two results of controllability to trajectories …
nonnegativity constraint on the state. We establish two results of controllability to trajectories …
Controllability of a class of infinite dimensional systems with age structure.
Given a linear dynamical system, we investigate the linear infinite dimensional system
obtained by grafting an age structure. Such systems appear essentially in population …
obtained by grafting an age structure. Such systems appear essentially in population …
[HTML][HTML] Approximate controllability of the FitzHugh-Nagumo equation in one dimension
Abstract The FitzHugh-Nagumo (FHN) equation is a simplified model of a nerve axon. We
explore the controllability of this model using a localized interior control only for the first …
explore the controllability of this model using a localized interior control only for the first …