# Researcher in Applied Mathematics

## Contact information

**Email** : math.golive [at] gmail.com

## Research interests

- Partial differential equations, Integral equations
- Control theory and stabilization
- Spectral theory

## Curriculum Vitae

## Lecture notes (Shandong University)

Lecture n°1 (03/16/2017)

Lectures n°1-2 (03/17/2017)

Lectures n°1-3 (03/23/2017)

Lectures n°1-4 (03/24/2017)

Lectures n°1-5 (03/30/2017)

Lectures n°1-6 (03/31/2017)

Full lecture notes (04/13/2017)

## Articles in preparation

[10] Perturbations of some null-controllable systems, D. Araujo de Souza and G. Olive, in preparation (2018).

[9] Finite-time boundary stabilization of linear hyperbolic balance laws with coefficients depending on time and space, J.-M. Coron, L. Hu, G. Olive and P. Shang, in preparation (2018).

## Articles published in a peer-reviewed journal

[8] Compact perturbations of controlled systems, M. Duprez and G. Olive, Math. Control Relat. Fields 8 (2018), pp. 397-410.

[7] Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation J.-M. Coron, L. Hu and G. Olive, Automatica 84 (2017), pp. 95-100.

[6] Internal controllability of first order quasi-linear hyperbolic systems with a reduced number of controls, SIAM J. Control Optim. 55-1 (2017), pp. 300-323.

[5] Stabilization and controllability of first-order integro-differential hyperbolic equations, J.-M. Coron, L. Hu and G. Olive, J. Funct. Anal. 271 (2016), 3554-3587.

[4] Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null-controllability in cylindrical domains, SIAM J. Control Optim. 52 (2014), no. 5, 2970-3001.

[3] Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients, Math. Control Relat. Fields 4 (2014), no. 3, 263-287.

[2] Boundary approximate controllability of some linear parabolic systems, Evol. Equ. Control Theory 3 (2014), no. 1, 167-189.

[1] Null-controllability for some linear parabolic systems with controls acting on different parts of the domain and its boundary, Math. Control Signals Systems 23 (2012), no. 4, 257-280.

## Some conference talks

[T3] An introduction to linear control theory, “Seminar of Applied Mathematics — Jagiellonian University”, Krakow (Poland), November 2016. **Abstract:** This talk is an introduction to the basic concepts of control theory, with an opening towards the controllability of parabolic systems.

[T2] Stabilization and controllability of first-order integro-differential hyperbolic equations, “Nonlinear Partial Differential Equations and Applications — A conference in the honor of Jean-Michel CORON for his 60th birthday”, Paris (France), March 2016. **Abstract:** This talk presents the results of the article [5].

[T1] Controllability of parabolic systems, “From Open to Closed Loop Control”, Graz (Austria), June 2015. **Abstract:** This talk reviews some of the controllability issues for parabolic systems with less controls than equations.