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Group properties of equations of diffusive-dynamical boundary layer. (Russian) Zbl 0980.76069

Andreev, V. K. (ed.) et al., Symmetry and differential equations. Proceedings of the 2nd international conference, Krasnoyarsk, Russia, August 21-25, 2000. Krasnoyarsk: Institute of Computational Modelling, Krasnoyarsk State Univ., Krasnoyarsk State Academy of Architecture and Civil Engineering, International Academy of Sciences of High School, 241-244 (2000).
The Lie-Ovsyannikov group analysis is applied to find invariant solutions of the equations of diffusive boundary layer for Oberbeck-Boussinesq and microconvection models (buoyancy and viscosity forces are essential, but inertia forces and pressure gradient are negligible). The equations have the form \(u_x+v_y=0\), \((1-\lambda c)u_{yy}=c\), \((1-\lambda c)c_{yy}=uc_x+vc_y-\lambda c^2_y\), where \((u,v)\) is velocity vector, \(c\) is concentration, and \(\lambda\) is Boussinesq parameter.
For the entire collection see [Zbl 0956.00040].

MSC:

76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76R99 Diffusion and convection
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