  The origin of fast radio bursts remains a puzzle. Suggestions have been made
that they are produced within the Earth atmosphere, in stellar coronae, in
other galaxies or at cosmological distances. If they are extraterrestrial, the
implied brightness temperature is very high, and therefore, the induced
scattering places constraints on possible models. In this paper, constraints
are obtained on flares from coronae of nearby stars. It is shown that the radio
pulses with the observed power could not be generated if the plasma density
within and in the nearest vicinity of the source is as high as it is necessary
in order to provide the observed dispersion measure. However, one cannot
exclude a possibility that the pulses are generated within a bubble with a very
low density and pass through the dense plasma only in the outer corona.
