In the magnetohydrodynamics approximation, nonstationary processes in solar coronal structures are considered, which are identified as compression waves. To study the rapid damping of these waves, the effects of heat conduction and radiation losses are applied, more precisely, the effect of the imbalance between heating and energy losses. The behavior of the waves varies greatly depending on the parameters of the coronal loops, which requires accuracy in their determination. The calculation results also depend on the accuracy of the heating/loss function approximation. Depending on these conditions, both the thermal conductivity effect and the imbalance between heating and energy losses can play a decisive role in the attenuation of slow magnetosonic waves. The effects of heat conduction and imbalance between heating and losses lead not only to wave attenuation, but also to its dispersion.
$^1$Kalmyk state university named after Gorodovikov