Abstract
In present paper, we deal with a backward diffusion problem for a time-fractional diffusion problem with a nonlinear source in a strip domain. We all know this nonlinear problem is severely ill-posed, i.e., the solution does not depend continuously on the measurable data. Therefore, we use the Fourier truncation regularization method to solve this problem. Under an a priori hypothesis and an a priori regularization parameter selection rule, we obtain the convergence error estimates between the regular solution and the exact solution at 0 ≤ x < 1 .
Highlights
Fractional diffusion problems have become important in engineering and science [1]
In [21], a new modified regularization method can be used to solve the backward problem for the nonlinear space-fractional diffusion equation
In [22], two new modified regularization methods are applied to solve the backward problem for a nonlinear Riesz–Feller space fractional diffusion equation
Summary
Fractional diffusion problems have become important in engineering and science [1]. In [9], an iteration regularization method is used to consider the inverse heat conduction problem for a time-fractional diffusion equation. In [13], the spectral regularization method is used to solve the Cauchy problem of the time-fractional advection-dispersion equation. In [14], a new regularization method is applied to solve a time-fractional inverse diffusion problem. In [15], the optimal regularization method is used to solve an inverse heat conduction problem for the fractional diffusion equation. In [21], a new modified regularization method can be used to solve the backward problem for the nonlinear space-fractional diffusion equation. In [22], two new modified regularization methods are applied to solve the backward problem for a nonlinear Riesz–Feller space fractional diffusion equation.
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