Approximate controllability from the exterior of space-time fractional diffusive equations

M Warma - SIAM Journal on Control and Optimization, 2019 - SIAM
Let Ω⊂R^N be a bounded domain with a Lipschitz continuous boundary. We study the
controllability of the space-time fractional diffusive equation {\mathbbD_t^αu+ …

Controllability of the one-dimensional fractional heat equation under positivity constraints

U Biccari, M Warma, E Zuazua - ar** nonlocal wave equations
M Warma, S Zamorano - ESAIM: Control, Optimisation and Calculus …, 2020 - esaim-cocv.org
We make a complete analysis of the controllability properties from the exterior of the
(possible) strong dam** wave equation associated with the fractional Laplace operator …

Control and numerical approximation of fractional diffusion equations

U Biccari, M Warma, E Zuazua - Handbook of Numerical Analysis, 2022 - Elsevier
The aim of this chapter is to give a broad panorama of the control properties of fractional
diffusive models from a numerical analysis and simulation perspective. We do this by …

Controllability properties from the exterior under positivity constraints for a 1-d fractional heat equation

H Antil, U Biccari, R Ponce, M Warma… - arxiv preprint arxiv …, 2019 - arxiv.org
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 …

Exponential turnpike property for fractional parabolic equations with non-zero exterior data

M Warma, S Zamorano - ESAIM: Control, Optimisation and Calculus …, 2021 - esaim-cocv.org
We consider averages convergence as the time-horizon goes to infinity of optimal solutions
of time-dependent optimal control problems to optimal solutions of the corresponding …

Exterior controllability properties for a fractional Moore–Gibson–Thompson equation

C Lizama, M Warma, S Zamorano - Fractional Calculus and Applied …, 2022 - Springer
The three concepts of exact, null and approximate controllabilities are analyzed from the
exterior of the Moore–Gibson–Thompson equation associated with the fractional Laplace …

Multiplicity of solutions for fractional -laplacian equations

R Abita, U Biccari - Journal of Elliptic and Parabolic Equations, 2023 - Springer
In this paper, we deal with the following elliptic-type problem (-Δ) q (·) s (·) u+ λ V u= α up (·)-
2 u+ β uk (·)-2 u in Ω, u= 0 in R n\Ω, where q (·): Ω¯× Ω¯→ R is a measurable function and s …

Multiplicity of solutions for fractional -Laplacian equations

A Rahmoune, U Biccari - arxiv preprint arxiv:2103.12600, 2021 - arxiv.org
In this paper, we deal with the following elliptic type problem $$\begin {cases}(-\Delta) _ {q
(.)}^{s (.)} u+\lambda Vu=\alpha\left\vert u\right\vert^{p (.)-2} u+\beta\left\vert u\right\vert^{k (.) …