  Heating by the central star is one of the key factors determining the
physical structure of protoplanetary disks. Due to the large optical thickness
in the radial direction, disk midplane regions are heated by the infrared
radiation from the disk surface (atmosphere), which in turn is directly heated
by the star. It was previously shown that interception of the stellar radiation
by inhomogeneities on the disk surface can cause perturbations that propagate
towards the star. In this work, we investigate the occurrence of such waves
within a detailed 1+1D numerical model of the protoplanetary disk. We confirm
the previous findings that in the disk, that is optically thick to its own
radiation, the surface perturbations indeed occur and propagate towards the
star. However, contrary to some analytical predictions, the thermal waves in
sufficiently massive disks affect only the upper layers without significant
fluctuations of temperature in the midplane. Our results indicate the need to
study this instability within more consistent hydrodynamic models.
