  Using a global 3D, fully self-consistent, multi-fluid hydrodynamic model, we
simulate the escaping upper atmosphere of the warm Neptune GJ436b, driven by
the stellar XUV radiation impact and gravitational forces and interacting with
the stellar wind. Under the typical parameters of XUV flux and stellar wind
plasma expected for GJ436, we calculate in-transit absorption in Ly{\alpha} and
find that it is produced mostly by Energetic Neutral Atoms outside of the
planetary Roche lobe, due to the resonant thermal line broadening. At the same
time, the influence of radiation pressure has been shown to be insignificant.
The modelled absorption is in good agreement with the observations and reveals
such features as strong asymmetry between blue and red wings of the absorbed
Ly{\alpha} line profile, deep transit depth in the high velocity blue part of
the line reaching more than 70%, and the timing of early ingress. On the other
hand, the model produces significantly deeper and longer egress than in
observations, indicating that there might be other processes and factors, still
not accounted, that affect the interaction between the planetary escaping
material and the stellar wind. At the same time, it is possible that the
observational data, collected in different measurement campaigns, are affected
by strong variations of the stellar wind parameters between the visits, and
therefore, they cannot be reproduced altogether with the single set of model
parameters.
