On Monday 10 June at 10:15 in MH:333, Nils Thorin will present his MSc thesis "Asymptotics of the Klein-Gordon equation using the method of stationary phase".

Abstract: To model the behaviour of particles and waves mathematically, partial differential equations are often used. They facilitate the study of changes in both space and time, and it is often interesting to find out how a system behaves asymptotically in time. The Klein-Gordon equation is a relativistic wave equation which models a relativistic spin-free particle. In this thesis we investigate the asymptotic behaviour of the linear Klein-Gordon equation with a rapidly decaying potential in one space dimension. This is done by first studying the case with zero potential and finding asymptotic estimates using the method of stationary phase. This is a method which makes it possible to determine the asymptotic behaviour of integrals of rapidly oscillating functions. Then the distorted Fourier transform is defined using tools from scattering theory, which transforms the Klein-Gordon equation into the zero potential case. Finally we state asymptotic bounds of the solution, which for bounded regions in space are almost identical to the results for the zero potential.

Supervisors: Sara Maad Sasane and Wilhelm Treschow

Examiner: Mikael Persson Sundqvist

All are welcome to attend!