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<p>In this paper, we adopt a quasi-boundary-value method to solve the nonlinear space-fractional backward problem with perturbed both final value and variable diffusion coefficient in general dimensional space, which is a severely ill-posed problem. The existence, uniqueness and stability of the solution for the quasi-boundary-value problem are proved. Convergence estimates are presented under an <i>a-priori</i> bound assumption of the exact solution. Finally, several numerical examples are given by the finite difference scheme and the fixed-point iteration method to show the effectiveness of the theoretical results.</p>

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A quasi-boundary-value method for solving a nonlinear space-fractional backward diffusion problem

  • 期刊论文

  • 发表日期：

    2025年3月31日

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  • Xiaoli Feng,
  • Xiaoyu Yuan,
  • Yun Zhang

摘要

In this paper, we adopt a quasi-boundary-value method to solve the nonlinear space-fractional backward problem with perturbed both final value and variable diffusion coefficient in general dimensional space, which is a severely ill-posed problem. The existence, uniqueness and stability of the solution for the quasi-boundary-value problem are proved. Convergence estimates are presented under an a-priori bound assumption of the exact solution. Finally, several numerical examples are given by the finite difference scheme and the fixed-point iteration method to show the effectiveness of the theoretical results.