WP4-SINV

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation

R. Bianchini, Crin-Barat T., M. Paicu. Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation (2022) Abstract. We prove the nonlinear asymptotic stability of stably stratified solutions…

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Esteve C., Zuazua E.. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws (2022) Abstract. We give a full characterization of the range of the operator which…

Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System

Crin-Barat T., L. Shou. Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System (2022) Abstract. In this paper we study the diffusive relaxation limit of the Jin-Xin system toward viscous…

On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

Crin-Barat T., De Nitti N., Zuazua E.. On the decay of one-dimensional locally and partially dissipated and hyperbolic systems (2022) Abstract. We study the time-asymptotic behavior of linear hyperbolic systems…

Differentiability with respect to the initial condition for Hamilton-Jacobi equations

Esteve C., Zuazua E.. Differentiability with respect to the initial condition for Hamilton-Jacobi equations (2021) Abstract. We prove that the viscosity solution to a Hamilton-Jacobi equation with a smooth convex…

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

descriptor systems, linear systems, long time behavior, optimal control, Riccati equations

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., Vol. 59.5 (2021), pp. 3600-3624 Abstract.…

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Hamilton-Jacobi equation, inverse design problem, obstacle problems, 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 Abstract. We study the inverse…

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

Adjoint problem, Diffusion–advection equation, Inverse problems, optimal control, Optimization

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 an algorithm for the time-inversion…

DyCon blog: Inverse problem for Hamilton-Jacobi equations

Spain. 03.04.2020. Today, our team member Carlos Esteve made a contribution to the DyCon Blog about "Inverse problem for Hamilton-Jacobi equations": Inverse design problem for Hamilton-Jacobi equations: projection on the…

A controlled multiscale model for traffic regulation via autonomous vehicles

T. Liard, . A controlled multiscale model for traffic regulation via autonomous vehicles. (2019) Abstract. Autonomous vehicles ($AV$s) allow new ways of regulating the traffic flow on road networks. Most…

On entropic solutions to conservation laws coupled with moving bottlenecks

T. Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. (2019) Abstract. Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled…

Optimal driving strategies for traffic control with autonomous vehicles

T. Liard, Raphael Stern, Maria Laura Delle Monache. Optimal driving strategies for traffic control with autonomous vehicles. IFAC-PapersOnLine 53.2 (2020), pp. 5322-5329 Abstract. This article considers the possibility of using…

Inverse design for the one-dimensional Burgers equation

T. Liard, E. Zuazua. Inverse design for the one-dimensional Burgers equation. (2019) Abstract. In this paper, we study the problem of inverse design for the one-dimensional Burgers equation. This problem…

Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature

C. Esteve Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvatureJ MATH PURE APPL, Vol 137 (2020) pp. 143-177, DOI: 10.1016/j.matpur.2019.12.006 Abstract. We consider…

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System

On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

Differentiability with respect to the initial condition for Hamilton-Jacobi equations

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

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

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

DyCon blog: Inverse problem for Hamilton-Jacobi equations

A controlled multiscale model for traffic regulation via autonomous vehicles

On entropic solutions to conservation laws coupled with moving bottlenecks

Optimal driving strategies for traffic control with autonomous vehicles

Inverse design for the one-dimensional Burgers equation

Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature

2D inverse design of linear transport equations on unstructured grids

Conservation laws in the presence of shocks

Inverse design and control in the presence of singularities (SINV)

Optimal actuator design via Brunovsky’s normal form

Stability and Convergence of a Randomized Model Predictive Control Strategy

Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

Control of certain parabolic models from biology and social sciences

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation