EXACT-SOLUTIONS FOR NONLINEAR DIFFUSION WITH NONLINEAR LOSS

Exact similarity solutions are developed for nonlinear diffusion with nonlinear reactive or irreversible absorptive loss from an instantaneo us source. The diffusivity is proportional to a power m of concentrati on, with 0 < m less-than-or-equal-to 1; and loss rate is also proporti onal to a power of concentration, n, with 0 less-than-or-equal-to n < 1. The solutions are for an arbitrary number of dimensions s > 0 with s = 1, 2, 3 in physical applications. All solutions give the slug radi us finite, increasing to a maximum, and then decreasing to zero in fin ite time. With n < 1, the loss rate at small concentrations is large e nough to ensure slug extinction in finite time. The corresponding exac t solutions for gain, not loss, are given also. They become independen t of initial slug quantity in the limit of infinite time.