Dispersion for the wave equation outside of a cylinder
A talk in the Oberseminar Analysis series by
Felice Iandoli
| Abstract: | In this talk I will present a recent result in collaboration with Oana Ivanovici (CNRS and Sorbonne Université). We consider the linear wave equation in the three dimensional Euclidean space with the presence of a cylindrical obstacle. We construct a sharp, global in time, parametrix which enables us to prove sharp dispersive estimates for the flow. This is the first result of this kind in the case that the curvature of the obstacle is not strictly positive. The main difficulty, in the case of problems at the exterior of convex obstacles, comes from rays which are tangent to the surface and that may cause diffraction phenomena. For obstacles with positive curvature, those tangent rays are perfectly described by the microlocal pararametrix of Melrose and Taylor in terms of Airy functions. In our case we shall use Bessel functions. Zoom Meeting ID: 986 0677 6055 Passcode: 430747 $\href{https://uni-bielefeld.zoom.us/j/98606776055?pwd=azBFdUVaQnJMU01tWjZUVEdxN2x5Zz09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A1 |