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We examine travelling wave solutions of the Porous-Fisher model, $\partial_tu(x,t)= u(x,t)\left[1-u(x,t)\right] + \partial_x \left[u(x,t) \partial_xu(x,t)\right]$, with a Stefan-like condition at the moving front, $x=L(t)$.Travelling wave solutions of this model have several novel characteristics.These travelling wave solutions: (i) move with a speed that is slower than themore standard Porous-Fisher model, $c<1/\sqrt{2}$; (ii) never lead topopulation extinction; (iii) have compact support and a well-defined movingfront, and (iv) the travelling wave profiles have an infinite slope at themoving front. Using asymptotic analysis in two distinct parameter regimes, $c\to 0^+$ and $c \to 1/\sqrt{2}\,^-$, we obtain closed-form mathematicalexpressions for the travelling wave shape and speed. These approximationscompare well with numerical solutions of the full problem.

New travelling wave solutions of the Porous-Fisher model with a moving boundary