Symmetries and Exact Solutions of Third-Order Partial Differential Equations Arising in the Impulsive Motion of a Flat Plate

The Lie-group formalism is applied to investigate the symmetries of the third-order partial differential equations arising in the impulsive motion of a flat plate. The governing equations is u_t = au_yy + bu_yyt, where u (y, t) denotes a real valued function, with spatial variable y and temporal variable t, both non-negative. We derived the infinitesimals that admit the classical symmetry group. The reduced ordinary differential equation is further studied and tried to obtain some exact solutions.