Time Lag in Transport Theory

Abstract

The time lag in the attainment of a stationary state or flow is defined for a class of linear and nonlinear transport equations. It is shown that the explicit calculation of the time lag can be reduced, for these equations, to the determination of the Green's function of a simpler, linear, time‐independent boundary‐value problem. For a linear transport equation knowledge of this Green's function enables one to recursively calculate certain time moments which afford an approximate representation of the solution. The possibility of an asymptotic exponential approach to the steady‐state solution of these linear transport equations is directly related to the convergence of the sequence of these time moments. An explicit example of a nonlinear diffusion in a finite system is used to illustrate the general theory. Certain properties of the time lag for the flux of this nonlinear diffusion problem are derived in the Appendix.