A General Regularization Principle

We study an inverse problem for two-dimensional fractional difusion equation,which is severely ill-posed. Relative to the case of one-dimension, the theoreti-cal analysis and numerical computation is more difcult. We use four diferentmethods, including static Fourier method, dynamic Fourier method, Tikhonov reg-ularization method, modifed quasi-boundary method. Finally, via these methods,we summarize a general regularization principle: Fα(x, a, b) is a kernel, which satis-fes: limαâ†'0Fα(x, a, b)=1;|Fα(x, a, b)|≤H(α), where H(α) is bounded.Although we consider an inverse problem for two-dimensional fractional difu-sion equation, the general principle can be applied to many other ill-posed problems,such as backward heat conduction problem, inverse problems for one-dimensionalfractional difusion equation.