  We examine travelling wave solutions of the Porous-Fisher model, $\partial_t
u(x,t)= u(x,t)\left[1-u(x,t)\right] + \partial_x \left[u(x,t) \partial_x
u(x,t)\right]$, 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 the
more standard Porous-Fisher model, $c<1/\sqrt{2}$; (ii) never lead to
population extinction; (iii) have compact support and a well-defined moving
front, and (iv) the travelling wave profiles have an infinite slope at the
moving front. Using asymptotic analysis in two distinct parameter regimes, $c
\to 0^+$ and $c \to 1/\sqrt{2}\,^-$, we obtain closed-form mathematical
expressions for the travelling wave shape and speed. These approximations
compare well with numerical solutions of the full problem.
