An approach to solutions of coupled semilinear partial differential equations with applications

In this work, an approach for finding the solution of coupled semi‐linear diffusion equations for initial value problems is presented. The formal exact solution is found and the Picard iteration is constructed. It is shown that the constructed sequence of solutions converges uniformly for some classes of initial value problems. The problem of dispersion of an oxygen demanding pollutant released into a uniform flow is studied. Copyright © 2000 John Wiley & Sons, Ltd.