Recent Herschel and ALMA observations of Photodissociation Regions (PDRs) have revealed the presence of a high thermal pressure (P ~ 10^7-10^8 K cm-3) thin compressed layer at the PDR surface where warm molecular tracer emission (e.g. CH+, SH+, high-J CO, H2,...) originate. These high pressures (unbalanced by the surrounding environment) and a correlation between pressure and incident FUV field (G0) seem to indicate a dynamical origin with the radiation field playing an important role in driving the dynamics. We investigate whether photoevaporation of the illuminated edge of a molecular cloud could explain these high pressures and pressure-UV field correlation. We developed a 1D hydrodynamical PDR code coupling hydrodynamics, EUV and FUV radiative transfer and time-dependent thermo-chemical evolution. We applied it to a 1D plane-parallel photoevaporation scenario where a UV-illuminated molecular cloud can freely evaporate in a surrounding low-pressure medium. We find that photoevaporation can produce high thermal pressures and the observed P-G0 correlation, almost independently from the initial gas density. In addition, we find that constant-pressure PDR models are a better approximation to the structure of photoevaporating PDRs than constant-density PDR models, although moderate pressure gradients are present. Strong density gradients from the molecular to the neutral atomic region are found, which naturally explain the large density contrasts (1-2 orders of magnitude) derived from observations of different tracers. The photoevaporating PDR is preceded by a low velocity shock (a few km/s) propagating into the molecular cloud. Photoevaporating PDR models offer a promising explanation to the recent observational evidence of dynamical effects in PDRs.
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