Fractional Tikhonov Method And Mollification Method Of A Non-characteristic Cauchy Problem For A Parabolic Equation

Because the solution of the non-characteristic Cauchy problem of parabolic equation does not always exist,if it does exist,its solution depends discontinuously on the given Cauchy data,i.e.a small measurement error causes a great change in the solution.In this paper,fractional Tikhonov regularization method and mollification regularization method are used to solve the non-characteristic Cauchy problem of parabolic equation,and the prior and posterior regularization parameter selection rules and corresponding error estimation of the provided method are given.Finally,numerical experiments are carried out,and the numerical results show that the provided regularization method is effective and feasible.