TY - JOUR
TI - Multi-channel scattering theory: large time asymptotics of Schrödinger type equations with general data
DO - https://doi.org/doi:10.7282/t3-qeas-fj24
PY - 2023
AB - This thesis appears to focus on scattering theory for both Schrödinger-type equations and Klein-Gordon equations. Chapter 1 provides an introduction to the background of the thesis, while Chapter 2 investigates the long-time behavior of solutions to the Schrödinger equation. Chapter 3 focuses on the construction of solutions to Schrödinger equations with non-trivial weakly localized parts, asymptotic self-similar solutions as time goes to infinity. Chapter 4 studies the long-time behavior of solutions to Klein-Gordon equations. In Chapter 5, the author presents a proof of Local Decay Estimates for Schrödinger-type equations. Finally, Chapter 6 establishes the $L^p$ boundedness of wave operators for linear Schrödinger equations with time-dependent potentials and provides applications of this result to nonlinear dispersive equations and Hartree nonlinear Schrödinger equations.
KW - Mathematics
KW - Scattering (Mathematics)
KW - Schrödinger equation
LA - English
ER -