A method of construction of solution for acoustic-gravity waves (AGW) above a wave source, taking dissipation throughout the atmosphere into account (Dissipative Solution above Source, DSAS), is proposed. The method is to combine three solutions for three parts of the atmosphere: an analytical solution for the upper isothermal part and numerical solutions for the real non-isothermal dissipative atmosphere in the middle part and for the real non-isothermal small dissipation atmosphere in the lower one. In this paper the method has been carried out for the atmosphere with thermal conductivity but without viscosity. The heights of strong dissipation and the total absorption index in the regions of weak and average dissipation are found. For internal gravity waves the results of test calculations for an isothermal atmosphere and calculations for a real non-isothermal atmosphere are shown in graphical form. An algorithm and appropriate code to calculate DSAS, taking dissipation due to finite thermal conductivity into account throughout the atmosphere, are developed. The results of test DSAS calculations for an everywhere isothermal atmosphere are given. The calculation results for DSAS for the real non-isothermal atmosphere are also presented. A method for constructing of the 2x2 Greens matrix fully taking dissipation into account and allowing to find disturbance from some source of AGW in the atmosphere is proposed.
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