2026/07/24 by Siwar Ben Said
#math.AP
Understanding the transport of semiclassical measures along generalized bicharacteristics is a key ingredient in the proof of observability for the wave equation. Here, the coefficients are only assumed to be of class C1, which is a limit case for the existence of bicharacteristics. We consider boundary conditions of the form ∂νu + i ∂t u = 0, as a first step towards more general Lopatinskii-type conditions. We derive the transport equation satisfied by the measure arising from the concentration of high-frequency waves that obstruct observability. Observability of solutions associated with positive time-frequencies is then obtained by contradiction under the geometrical control condition.