The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion coefficient is the smaller and if the nonlinear term f(y) grows slower than |y|log3/2(1+|y|) at infinity. In the proof we use null controllability results for the associate linear system and global Carleman estimates with explicit bounds or combinations of several of these estimates. In order to treat the terms appearing on the interface, we have to construct specific weight functions depending on geometry.

We present ALMA 1.3 mm continuum observations at (25 au) resolution of Elias 2–24, one of the largest and brightest protoplanetary disks in the Ophiuchus Molecular Cloud, and we report the presence of three partially resolved concentric gaps located at ∼20, 52, and 87 au from the star. We perform radiative transfer modeling of the disk to constrain its surface density and temperature radial profile and place the disk structure in the context of mechanisms capable of forming narrow gaps such as condensation fronts and dynamical clearing by actively forming planets. In particular, we estimate the disk temperature at the locations of the gaps to be 23, 15, and 12 K (at 20, 52, and 87 au, respectively), very close to the expected snowlines of CO (23–28 K) and N₂ (12–15 K). Similarly, by assuming that the widths of the gaps correspond to 4–8× the Hill radii of forming planets (as suggested by numerical simulations), we estimate planet masses in the range of , , and for the inner, middle, and outer gap, respectively. Given the surface density profile of the disk, the amount of “missing mass” at the location of each one of these gaps (between 4 and 20 ) is more than sufficient to account for the formation of such planets.