Abstract
Exact solutions are developed for nonlinear diffusion with first-order loss (e.g. by reaction, irreversible absorption, biological degradation, or radioactive decay) from an instantaneous source. The diffusivity is proportional to a positive power of concentration. The solutions are for an arbitrary number of dimensions s > 0, with s = 1,2,3 in physical applications. All solutions give the slug radius exponentially approaching a finite maximum, with concentration decreasing exponentially to zero. Applications include the gravity spreading, and ultimate extinction, of liquid lenses on solid, or immiscible liquid, surfaces. The corresponding exact solutions for first-order gain, not loss, are also given.
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