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We examine travelling wave solutions of the reaction-diffusion equation,$\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$, with aStefan-like condition at the edge of the moving front. With only a fewassumptions on $R(u)$ and $D(u)$, a variety of new compactly supportedtravelling waves arise in this Reaction-Diffusion Stefan model. While otherreaction-diffusion models admit compactly supported travelling waves for aunique wavespeed, we show that compactly supported travelling waves in theReaction-Diffusion Stefan model exist over a range of wavespeeds. Furthermore,we determine the necessary conditions on $R(u)$ and $D(u)$ for which compactlysupported travelling waves exist for all wavespeeds. Using asymptotic analysisin various distinguished limits of the wavespeed, we obtain approximatesolutions of these travelling waves, agreeing with numerical simulations withhigh accuracy.

Compactly supported travelling waves arising in a general reaction-diffusion Stefan model