#### Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions

Y. Privat, E. Trélat & E. Zuazua. Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions, DOI: 10.1007/s00526-019-1522-3. Abstract: We consider a spectral optimal design problem involving the Neumann traces of the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset Ω of IRn. The cost functional measures the amount of energy that Dirichlet…

#### Dynamics and control for multi-agent networked systems: a finite difference approach

U. Biccari, D. Ko, E. Zuazua Dynamics and control for multi-agent networked systems: a finite difference approach Abstract: We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations commonly derived as the…

#### Phase portrait control for 1D monostable and bistable reaction-diffusion equations

Pouchol C., Trélat E., Zuazua E. Phase portrait control for 1D monostable and bistable reaction-diffusion equations , DOI: 10.1088/1361-6544/aaf07e Abstract: We consider the problem of controlling parabolic semilinear equations arising in population dynamics, either in finite time or infinite time. These are the monostable and bistable equations on (0,L) for a density of individuals 0≤y(t,x)≤1,…

#### Internal observability for coupled systems of linear partial differential equations

Lissy, P., Zuazua, E. Internal observability for coupled systems of linear partial differential equations , DOI: 10.1137/17M1119160 Abstract: We deal with the internal observability for some coupled systems of partial differential equations with constant or time-dependent coupling terms by means of a reduced number of observed components. We prove new general observability inequalities under some…

#### A Two-Dimensional “Flea on the Elephant” Phenomenon and its Numerical Visualization

Bianchini, R., Gosse, L., Zuazua, E. A two-dimensional “flea on the elephant” phenomenon and its numerical visualization , Multiscale Modeling & Simulation, Vol. 17, No. 1 (2019), pages 137–166, DOI: 10.1137/18M1179985. Abstract: Localization phenomena (sometimes called “flea on the elephant”) for the operator $L ε = −ε 2 ∆u + p(x)u, p(x)$ being an unbounded…

#### Greedy optimal control for elliptic problems and its application to turnpike problems

Hernández-Santamaría V., Lazar M., Zuazua E. Greedy optimal control for elliptic problems and itsapplication to turnpike problems DOI: 10.1007/s00211-018-1005-z Abstract: We adapt and apply greedy methods to approximate in an efficient way the optimalcontrols for parameterized elliptic control problems. Our results yield an optimal approximation procedure that, in particular, performs better than simply sampling theparameter-space…