Ergodicity of reversible reaction diffusion processes

Summary Reaction-diffusion processes were introduced by Nicolis and Prigogine, and Haken. Existence theorems have been established for most models, but not much is known about ergodic properties. In this paper we study a class of models which have a reversible measure. We show that the stationary distribution is unique and is the limit starting from any initial distribution.The work was begun while the first author was visiting Cornell and supported by the Chinese government. The initial results (for Schlögl's first model) was generalized while the three authors were visiting the Nankai Institute for Mathematics, Tianjin, People's Republic of ChinaPartially supported by the National Science Foundation and the Army Research Office through the Mathematical Sciences Institute at Cornell UniversityPartially supported by NSF grant DMS 86-01800