A preliminary group classification of the class 2D nonlinear heat equations ut = f (x, y, uy)(uxx +uyy), where f is the arbitrary smooth function of the variables x, y, u, u_x and uy is given. Furthermore, we have proved that an optimal system of one-dimensional Lie subalgebras of this equation is generated by and we obtain Z~is in Theorem 4.1. Also we take their optimal system's projections on the space (x,y,u,ux,uy,f). The paper is one of the few applications of an algebraic approach to the problem of group classification using Lie method that is called the method of preliminary group classification.
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