Group classification of the dispersion equation of gaseous pollutants in presence of a temperature inversion

The Lie group method is applied to make a group classification of the PDE governs the dispersion of gaseous pollutants in the presence of a temperature inversion and obtained on a great varity of analytical solutions. The pollutants are assumed to be spread in the layer bounded by the ground surface and the inversion level and they are driven by wind in the horizontal direction. The general solution has been specified for two cases; (i) the ground absorbs all the gaseous pollutants and (ii) the ground does not absorb any pollutant.