In this talk, we consider the linear wave equation with the scale-invariant damping and mass. It is known by Wirth that the solution scatters to the solution of the modified wave equation. Our first aim is to investigate the asymptotic order. We also treat the corresponding equation with the energy critical nonlinearity. Our second aim is to obtain the scattering result and its asymptotic order. This talk is based on joint works [1] and [2] with Professor Haruya Mizutani (Osaka University).

References:

[1] T. Inui, H. Mizutani, "Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass", preprint, arXiv:2004.03832.

[2] T. Inui, H. Mizutani, "Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with $L^r$-data", preprint, arXiv:2005.01335.

Note: This seminar will be held as a Zoom online seminar.