摘要：We consider a Cauchy problem of unidimensional
nonlinear diffusion equation on finite interval. This problem is ill-posed
and its approximate solution is unstable. We apply the He's homotopy
perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has
a specified condition, the above solution can be estimated. Finally, a
numerical experiment is provided to illustrate the method.
