The 13 Myr old star HD106906 is orbited by a debris disk of at least 0.067 M_Moon with an inner and outer radius of 20 AU and 120 AU, respectively, and by a planet at a distance of 650 AU. We use this curious combination of a close low-mass disk and a wide planet to motivate our simulations of this system. We study the parameter space of the initial conditions to quantify the mass loss from the debris disk and its lifetime under the influence of the planet. We find that when the planet orbits closer to the star than about 50 AU and with low inclination relative to the disk (less than about 10 degrees), more disk material is perturbed outside than inside the region constrained by observations on timescales shorter than 1 Myr. Considering the age of the system, such a short lifetime of the disk is incompatible with the timescale for planet--planet scattering which is one of the scenarios suggested to explain the wide separation of the planet. For some configurations when the planets orbit is inclined with respect to the disk, the latter will start to wobble. We argue that this wobbling is caused by a mechanism similar to the Kozai--Lidov oscillations. We also observe various resonant structures (such as rings and spiral arms) induced in the disk by the planet.
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