In this paper, we focus our study on the implementation of a synchronous load balancing algorithm with an asynchronous PDE solver on heterogeneous and dynamic networks. The PDE (Partial Differential Equation) chosen formulates and solves the behavior of the concentration of two chemical species on a water plan. The load balancing algorithm implemented is the first order diffusion algorithm. Two main problems are studied in this paper. The first is the interaction between synchronism and asynchronism (synchronism with load balancing and asynchronism with computation). The second is the definition of the load balancing parameters for this solver in the dynamic context. For these two problems, we give various solutions and study their impacts on real experimentations.