We focus on shaping the long-term spatiotemporal dynamics of transport-reaction processes which can be described by semi-linear partial differential equations (PDEs). The dynamic shaping problem is addressed via error dynamics regulation between the governing PDE and a target PDE which describes the desired spatiotemporal behavior. A model order reduction methodology is utilized to construct the required reduced order models (ROMs) for governing and target dynamics via Galerkin's method. We subtract the governing from the target ROMs to obtain reduced offset dynamics error. Then an output feedback sliding mode control structure is synthesized to stabilize the reduced error dynamics and correspondingly synchronize the system and the target spatiotemporal behaviors. A Luenberger-type dynamic observer is applied to estimate the states of the governing ROM required by the sliding mode controller. The proposed approach is applied to address the thermal spatiotemporal dynamic shaping problem in a tubular chemical reactor. (C) 2015 Elsevier Ltd. All rights reserved.