Sampling gas distributions by robotic platforms in order to find gas sources is an appealing approach to alleviate threats for a human operator. Different sampling strategies for robotic gas exploration exist. In this paper we investigate the benefit that could be obtained by incorporating physical knowledge about the gas dispersion. By exploring a gas diffusion process using a multi-robot system. The physical behavior of the diffusion process is modeled using a Partial Differential Equation (PDE) which is integrated into the exploration strategy. It is assumed that the diffusion process is driven by only a few spatial sources at unknown locations with unknown intensity. The objective of the exploration strategy is to guide the robots to informative measurement locations and by means of concentration measurements estimate the source parameters, in particular, their number, locations and magnitudes. To this end we propose a probabilistic approach towards PDE identification under sparsity constraints using factor graphs and a message passing algorithm. Moreover, message passing schemes permit efficient distributed implementation of the algorithm, which makes it suitable for a multi-robot system. We designed an experimental setup that allows us to evaluate the performance of the exploration strategy in hardware-in-the-loop experiments as well as in experiments with real ethanol gas under laboratory conditions. The results indicate that the proposed exploration approach accelerates the identification of the source parameters and outperforms systematic sampling. (C) 2019 Elsevier B.V. All rights reserved.