Exact stationary and autowave solutions in minimal models of a bistable medium (Q1603182)

This paper deals with the minimal deterministic models of homogeneous and heterogeneous bistable media. The author finds stationary and autowave solutions and derives conditions for the existence of such solutions in elementary functions. The model presented by the author permits to find the exact critical size of an inhomogeneity for the forced heterogeneous nucleation of a new stable state from a metastable state and to obtain exact conditions under which the autowave of transition from the metastable state to the new stable state can be arrested by a local imperfection of the medium.