Author

E. Zuazua

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Preprint Sep 2026

Crossover asymptotics and a sharp confinement rate for the viscous Burgers equation

We study the one-dimensional viscous Burgers equation on $(0,L)$ with the conservative boundary conditions $u_x=-u^2$. On the half-line, solutions approach a nonlinear self-similar profile, whereas on a bounded interval they converge to a nonconstant equilibrium. We describe explicitly how the dynamics passes between t...

M. Sônego, E. Zuazua · 0 citations

Preprint Sep 2026

Two-term small-time spectral expansions for controllability Gramians

For a controllable single-input linear system in dimension $n$, the controllability Gramian eigenvalues, ordered decreasingly, are known to have the successive small-time orders $T, T^3, \ldots, T^{2n-1}$. We refine this leading-order hierarchy by explicitly computing the next-order coefficient of every eigenvalue and...

Emmanuel Tr'elat Ljll, Ca Ge, E. Zuazua · 1 citation · ⚡1