Abstract
This paper is devoted to recovering simultaneously the fractional order and the space-dependent source term from partial Cauchy’s boundary data in a multidimensional time-fractional diffusion equation. The uniqueness of the inverse problem is obtained by employing analytic continuation and the Laplace transform. Then a modified non-stationary iterative Tikhonov regularization method with a regularization parameter chosen by a sigmoid-type function is used to find a stable approximate solution for the source term and the fractional order. Numerical examples in one-dimensional and two-dimensional cases are provided to illustrate the efficiency of the proposed algorithm.
Funding statement: This work is supported by the Youth Science and Technology Fund of Gansu Province (grant no. 20JR10RA099), the Innovation Capacity Improvement Project for Colleges and Universities of Gansu Province (grant no. 2020B-088), the Young Teachers’ Scientific Research Ability Promotion Project of NWNU (grant no. NWNU-LKQN-18-31) and the Doctoral Scientific Research Foundation of NWNU (grant no. 6014/0002020204).
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Parameter identification for portfolio optimization with a slow stochastic factor
- Simultaneous inversion of a fractional order and a space source term in an anomalous diffusion model
- On the inverse gravimetry problem with minimal data
- On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission
- Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems
- Convergence analysis of iteratively regularized Gauss–Newton method with frozen derivative in Banach spaces
- Identification of an unknown flexural rigidity of a cantilever Euler–Bernoulli beam from measured boundary deflection
- Hadamard’s example and solvability of the mixed Cauchy problem for the multidimensional Gellerstedt equation
- Ill-posed problems and the conjugate gradient method: Optimal convergence rates in the presence of discretization and modelling errors
- Simultaneous determination of mass density and flexural rigidity of the damped Euler–Bernoulli beam from two boundary measured outputs
Articles in the same Issue
- Frontmatter
- Parameter identification for portfolio optimization with a slow stochastic factor
- Simultaneous inversion of a fractional order and a space source term in an anomalous diffusion model
- On the inverse gravimetry problem with minimal data
- On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission
- Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems
- Convergence analysis of iteratively regularized Gauss–Newton method with frozen derivative in Banach spaces
- Identification of an unknown flexural rigidity of a cantilever Euler–Bernoulli beam from measured boundary deflection
- Hadamard’s example and solvability of the mixed Cauchy problem for the multidimensional Gellerstedt equation
- Ill-posed problems and the conjugate gradient method: Optimal convergence rates in the presence of discretization and modelling errors
- Simultaneous determination of mass density and flexural rigidity of the damped Euler–Bernoulli beam from two boundary measured outputs