In this talk, we consider inhomogeneous initial boundary value problems and introduce a unified approach for analyzing their solutions in fractional Sobolev spaces.  Our approach relies on obtaining representation formulas by using a modern transform method and applying basic tools of oscillatory integrals to these formulas.  We recover the well known results for the classical Schrödinger equation subject to Dirichlet b.c. in a simpler way and also extend the theory to other types of boundary conditions and related equations such as the fourth order Schrödinger equation.

This research is funded by TÜBİTAK'S 1001 Grant 117F449 and the Science Academy's Young Scientist award in Mathematics (BAGEP 2020).