Transient Solutions to Some Weakly Diffusive Nonlinear Diffusion Equations

摘要

A multiple time scale procedure is developed and used to describe the full transient behavior of solutions to certain classes of nonlinear diffusion initial value problems where the diffusion coefficients are in a certain sense “weak.” Specific examples are presented which demonstrate the explicit manner in which various traveling wave and oscillation patterns develop from arbitrary initial data for certain well‐known model systems in population biology and chemical kin