Many unmanned aerial vehicle (UAV) applications have been employed for performing data collection in facilitating tasks such as surveillance and monitoring objectives in remote and dangerous environments. In light of the fact that most of the existing UAV relaying applications operate in conventional half-duplex (HD) mode, a full-duplex (FD) based UAV relay aided wireless network is investigated, in which the UAV relay helps forwarding information from the source (S) node to the destination (D). Since the activated UAV relays are always floating and flying in the air, its channel state information (CSI) as well as channel capacity is a time-variant parameter. Considering decode-and-forward (DF) relaying protocol in UAV relays, the cooperative relaying channel capacity is constrained by the relatively weaker one (i.e. in terms of signal-to-noise ratio (SNR) or signal-to-interference-plus-noise ratio (SINR)) between S-to-relay and relay-to-D links. The channel capacity can be optimized by adaptively optimizing the transmit power of S and/or UAV relay. Furthermore, a hybrid HD/FD mode is enabled in the proposed UAV relays for adaptively optimizing the channel utilization subject to the instantaneous CSI and/or remaining self-interference (SI) levels. Numerical results show that the channel capacity of the proposed UAV relay aided wireless networks can be maximized by adaptively responding to the influence of various real-time factors.