B. Geshkovski, E. Zuazua. Controllability of one-dimensional viscous free boundary flows. Siam. J. Control. Optim (2021), Vol. 59, No. 3, pp. 1830–1850. https://doi.org/10.1137/19M1285354 Abstract. In…
View More Controllability of one-dimensional viscous free boundary flowsCategory: WP5-MHM
WP5: Models involving memory terms and hybrid PDE+ODE systems (MHM)
Control and Deep Learning: Some connections
B. Geshkovski, E. Zuazua. Control and Deep Learning: Some connections (2021) This note is an extended abstract for a talk given by the second author…
View More Control and Deep Learning: Some connectionsInternal control for a non-local Schrödinger equation involving the fractional Laplace operator
U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2021) Abstract: We analyze the interior controllability problem for a nonlocal…
View More Internal control for a non-local Schrödinger equation involving the fractional Laplace operatorNull-controllability of perturbed porous medium gas flow
B. Geshkovski,Null-controllability of perturbed porous medium gas flow. ESAIM:COCV, vol. 26, No. 85 (2020). DOI: 10.1051/cocv/2020009 Abstract: In this work, we investigate the null-controllability of…
View More Null-controllability of perturbed porous medium gas flowControllability of a Class of Infinite Dimensional Systems with Age Structure
Maity D., Tucsnak M., Zuazua E. Controllability of a Class of Infinite Dimensional Systems with Age Structure. Control Cybern. Vol. 48 (2020), No. 2, pp.…
View More Controllability of a Class of Infinite Dimensional Systems with Age StructureControllability of the one-dimensional fractional heat equation under positivity constraints
U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Commun. Pure Appl. Anal., Vol 19. No. 4 (2019), pp. 1949-1978. DOI: 10.3934/cppaa.2020086
View More Controllability of the one-dimensional fractional heat equation under positivity constraintsA PDE-ODE model for traffic control with autonomous vehicles
Thibault Liard, Raphael Stern, Maria Laura Delle Monache. A PDE-ODE model for traffic control with autonomous vehicles. (2020) Abstract. We introduce a coupled PDE-ODEs model…
View More A PDE-ODE model for traffic control with autonomous vehiclesNull-controllability properties of a fractional wave equation with a memory term
U. Biccari, M. Warma Null-controllability properties of a fractional wave equation with a memory term. Evol. Eq. Control The., Vol. 9, No. 2 (2020), pp.…
View More Null-controllability properties of a fractional wave equation with a memory termExistence and cost of boundary controls for a degenerate/singular parabolic equation
Umberto Biccari, Víctor Hernández-Santamaría, Judith Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation (2020). Abstract. In this paper, we consider the…
View More Existence and cost of boundary controls for a degenerate/singular parabolic equationPropagation of one and two-dimensional discrete waves under finite difference approximation
U. Biccari, A. Marica, E. Zuazua Propagation of one and two/dimensional discrete waves under finite difference approximation, Found. Comput. Math., Vol. 20 (2020), pp. 1401-1438.…
View More Propagation of one and two-dimensional discrete waves under finite difference approximationWKB expansion for a fractional Schrödinger equation with applications to controllability
Solving an optimal control problem arised in ecology with AMPL
WKB expansion for a fractional Schrödinger equation with applications to controllability
PDF version | Download Matlab Code… In [3], we develop a WKB analysis for the propagation of the solutions to the following one-dimensional nonlocal Schrödinger…
View More WKB expansion for a fractional Schrödinger equation with applications to controllabilityFinite element approximation of the 1-D fractional Poisson equation MATLAB code
Solving an optimal control problem arised in ecology with AMPL
PDF version… | Download Code… Introduction We are interested in optimal control problems subject to a class of diffusion-reaction systems that describes the growth and spread…
View More Solving an optimal control problem arised in ecology with AMPL
Finite element approximation of the 1-D fractional Poisson equation
A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control.
View More Finite element approximation of the 1-D fractional Poisson equation
Control of PDEs involving non-local terms
Relevant models in Continuum Mechanics, Mathematical Physics and Biology are of non-local nature. Moreover, these models are applied for the description of several complex phenomena for which a local approach is inappropriate or limiting. In this setting, classical PDE theory fails because of non-locality. Yet many of the existing techniques can be tuned and adapted, although this is often a delicate matter…
View More Control of PDEs involving non-local termsModels involving memory terms & hybrid PDE+ODE systems (MHM)
Control theory for PDEs has been quite exhaustively developed for model problems (heat and wave equations). But other important models in applications, of hybrid nature,…
View More Models involving memory terms & hybrid PDE+ODE systems (MHM)