چکیده (انگلیسی):

In this paper we utilize the method of invariant set to derive exact solutions of the two dimensional nonlinear reaction-diffusion equations with source term. It is shown that there exists a class of reaction-diffusion equations which are invariant with respect to the sets E1 = { u:ux = vxf (t)F (u); uy = vyf (t)F (u)} and E2 = {u : ux = a’(x)f (t)F (u); uy = b’(y)g(t)F (u)}, with f ≠ g. As a result, we obtain exact solutions of the certain nonlinear reaction-diffusion equations. These solutions extend the well-known self-similar solutions and instantaneous source type solutions of the porous medium equation. The behavior to some solutions and the corresponding interfaces are also described.