The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term

Shi Jin, Yuhua Zhu, Enrique Zuazua. The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term (2021) Numer Math (Heidelb) Abstract. We consider the Vlasov-Fokker-Planck equation…

View More The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term

Model predictive control with random batch methods for a guiding problem

Ko Dongnam, Zuazua Enrique. Model predictive control with random batch methods for a guiding problem (2021). Math. Models Methods Appl. Sci., Vol. 31, No. 8,…

View More Model predictive control with random batch methods for a guiding problem

Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

Heiland J., Zuazua E. Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems (2021) SIAM J. Control Optim. Abstract.…

View More Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms

M. Gugat, M. Schuster, E. Zuazua. The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms, in “Stabilization of Distributed Parameter Systems:…

View More The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms

Nonnegative control of finite-dimensional linear systems

Lohéac J., Trélat E., Zuazua E. Nonnegative control of finite-dimensional linear systems. Ann. I. H. Poincare-An., Vol. 38, No. 2, pp. 301-346. (2021) DOI: https://doi.org/10.1016/j.anihpc.2020.07.004…

View More Nonnegative control of finite-dimensional linear systems

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Esteve C., Zuazua E.. The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes SIAM J. Math. Anal., Vol. 52, No. 6, pp. 5627–5657 (2020). https://doi.org/10.1137/20M1330130…

View More The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations

Ruiz-Balet D., Zuazua E.. Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. J. Math. Pures Appl, vol. 143, pp. 345-375 (2020) https://doi.org/10.1016/j.matpur.2020.08.006 Abstract.…

View More Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations

Sparse source identification of linear diffusion–advection equations by adjoint methods

Monge A., Zuazua E. Sparse source identification of linear diffusion–advection equations by adjoint methods. Syst. Control. Lett, vol. 145 (2020). DOI: https://doi.org/10.1016/j.sysconle.2020.104801 Abstract: We present…

View More Sparse source identification of linear diffusion–advection equations by adjoint methods

Controllability 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 Structure

Shape turnpike for linear parabolic PDE models

Lance G., Trélat E., Zuazua E. Shape turnpike for linear parabolic PDE models  Syst. Control. Lett. Vol. 142 (2020). DOI: 10.1016/j.sysconle.2020.104733 Abstract: We introduce and…

View More Shape turnpike for linear parabolic PDE models

A stochastic approach to the synchronization of coupled oscillators

Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front. Energy Res. Vol. 8 (2020).…

View More A stochastic approach to the synchronization of coupled oscillators

Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions

J.-C. Cortes, A. Navarro-Quiles, J.-V. Romero, M.-D. Rosello, E. Zuazua. Full probabilistic solution of a infinite dimensional linear control system with random initial and final…

View More Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions

Asymptotic behavior and control of a “guidance by repulsion” model

Dongnam Ko, E. Zuazua, Asymptotic behavior and control of a “guidance by repulsion” model. Math Models Methods Appl. Sci. Vol. 30, No. 04, pp. 765-804…

View More Asymptotic behavior and control of a “guidance by repulsion” model

The turnpike property in nonlinear optimal control – A geometric approach

N. Sakamoto, D. Pighin, E. Zuazua The turnpike property in nonlinear optimal control – A geometric approach. IEEE 58th Conference on Decision and Control (CDC)…

View More The turnpike property in nonlinear optimal control – A geometric approach

Propagation 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 (2020). DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…

View More Propagation of one and two-dimensional discrete waves under finite difference approximation

Controllability 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 constraints

Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function

U. Biccari, E. Zuazua Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function J. Differential Equations,…

View More Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function
Wave composition

Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems

We analyze the inverse problem of identifying the diffusivity coefficient of a scalar elliptic equation as a function of the resolvent operator. We prove that, within the class of measurable coefficients, bounded above and below by positive constants, the resolvent determines the diffusivity in an unique manner…

View More Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems