Area grows faster than length, so the zombies eat you, as Joseph Van Name said.

It is sufficient for the zombies to form an uncrossable circular barrier enclosing you and then to shrink the circle till the catch you.

To form an uncrossable circular barrier, there need to be $2\pi r/d$ zombies. For the zombies to reach their position on the barrier before you can (taking your original position as the origin), they must have an initial radius between $r(1-v)$ and $r(1+v)$. The number of zombies in this region is $\pi r^2 \mu((1+v)^2-(1-v)^2)=4\pi r^2 \mu v$. Given $d, v, \mu$, take $r$ large enough, and the zombies easily form the circular barrier before you reach it.

Area grows faster than length, so the zombies eat you, as Joseph Van Name said.

It is sufficient for the zombies to form an uncrossable circular barrier enclosing you and then to shrink the circle till the catch you.

To form an uncrossable circular barrier, there need to be $2\pi r/d$ zombies. For the zombies to reach their position on the barrier before you can (taking your original position as the origin), they must have an initial radius between $r(1-v)$ and $r(1+v)$. The number of zombies in this region is $\pi r^2 \mu((1+v)^2-(1-v)^2)=4\pi r^2 \mu v$. Given $d, v, \mu$, take $r$ large enough, and the zombies easily form the circular barrier before you reach it.

EDIT: This does not answer the original question, as it allows the zombies to apply a strategy. In this strategy, all the zombies with initial radius between $(1-v)r$ and $r$, move away from the runner to form the circle, rather than directly towards the runner, as specified in the original question.