Varying boundary conditions with large diffusivity (Q762369)

For systems of semilinear parabolic partial differential equations on bounded domains with large diffusivity and homogeneous boundary conditions close to the Neumann conditions, we associate a system of ordinary differential equations (ode's) from which the dynamics of the original system can be inferred. Small perturbations of the Neumann case produce large perturbations in the ode's with corresponding effects on the dynamics of the system. The same theory is valid for functional differential equations. Applications are considered in models for control by genetic repression of biological material in cells.