Boundary effects play an interesting role in the finite-size physical systems.? Those are reminiscent of the choices of the boundary conditions. In this work,? we study? the boundary induced dynamical properties in the “1+1”-dimensional critical systems,? driven by the inhomogeneous quenches of SSD and M?bius types. We find that different boundary? conditions measured by the boundary entropy lead to different scenarios of phase transitions.?We give a holographic interpretation in terms of intersecting branes in AdS3.