Invariant sets and solutions to the generalized thin film equation

摘要

The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the setrnE_0 = {u : u_x = v_xF(u), u_y = v_yF(u)},rnwhere v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the 1+1-dimensional nonlinear evolution equations.