Exact renormalization group approach to a nonlinear diffusion equation.

The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an anomalous diffusion exponent in full order of the perturbation series with respect to a nonlinearity.