Context :

Aims : In this work we study the influence of the UV radiation field of a massive star on the evolution of a disklike mass of gas and dust around a nearby star .
This system has similarities with the proplyds seen in Orion .

Methods : We study disks with different inclinations and distances from the source , performing fully 3D numerical simulations .
We use the YGUAZÚ-A adaptative grid code modified to account for EUV/FUV fluxes and non-spherical mass distributions .
We treat H and C photoionization in order to reproduce the ionization fronts and photodissociation regions observed in proplyds .
We also incorporate a wind from the ionizing source , in order to investigate the formation of the bow shock observed in several proplyds .
We examine density and H \alpha maps , as well as the mass loss rates in the photoevaporated winds .

Results : Our results show that a photoevaporated wind propagates from the disk surface and becomes ionized after an ionization front ( IF ) seen as a bright peak in the H \alpha maps .
We follow the development of an HI region inside the photoevaporated wind which corresponds to a photodissociated region ( PDR ) for most of our models , except those without a FUV flux .
For disks that are at a distance from the source d \geq 0.1 pc , the PDR is thick and the IF is detached from the disk surface .
In contrast , for disks that are closer to the source , the PDR is thin and not resolved in our simulations .
The IF then coincides with the first grid points of the disk that are facing the ionizing photon source .
In both cases , the photoevaporated wind shocks ( after the IF ) with the wind that comes from the ionizing source , and this interaction region is bright in H \alpha .

Conclusions : Our 3D models produce two emission features : a hemispherically shaped structure ( associated with the IF ) and a detached bow shock where both winds collide .
A photodissociated region develops in all of the models exposed to the FUV flux .
More importantly , disks with different inclinations with respect to the ionizating source have relatively similar photodissociation regions .
If the disk axis is not aligned with the direction of the ionizing photon flux , the IF displays moderate side-to-side asymmetries , in qualitative agreement with images of proplyds , which also show such asymmetries .
The mass loss rates are \sim 10 ^ { -7 } M _ { \odot } yr ^ { -1 } for face-on disks , and 5 \times 10 ^ { -8 } M _ { \odot } yr ^ { -1 } for inclined disks at distances from 0.1 to 0.2 pc from the ionizing photon sources .