ABSTRACT
In connection with the many applications in physics, chemistry, biology, dissipative structures of different kinds which are described by stable spatially nonuniform solutions of system of nonlinear diffusion equations with sources have been intensively investigated theoretically and experimentally [215-217] . The theoretical investigations of dissipative structures are traditionally performed with the simplest matrix (diagonal, with constant elements) of transport coefficients but with complex (nonlinear) sources [218 - 221]. In the present chapter, on the contrary, the dissipative structures are considered which correspond to a system of diffusion equations with a non-diagonal and nonlinear matrix of transport coefficients but with a linear source [222,223]. The situation in a fuel element of a gas phase nuclear reactor [102] is simulated, where uranium is in the fuel element and heat generation is proportional to it's concentration in the plasma. The physical reason for the emergence of dissipative structures is the diffusion of the uranium to a region with higher temperature. This investigation is practically important for the thermal protection of surfaces in contact with a plasma in the fuel element and, also, for the problem of stability of the reactor operation.
