An alternating approach for reconstructing the initial value and source term in a time-fractional diffusion-wave equation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912242318966784 |
|---|---|
| author | Zhang, Yun Feng, Xiaoli Yan, Xiongbin |
| author_facet | Zhang, Yun Feng, Xiaoli Yan, Xiongbin |
| contents | This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem by leveraging the asymptotic expansion of Mittag-Leffler functions. Subsequently, we decompose the inverse problem into two subproblems and introduce an alternating iteration reconstruction method, complemented by a regularization strategy. Additionally, a comprehensive convergence analysis for this method is provided. To solve the inverse problem numerically, we introduce two semidiscrete schemes based on standard Galerkin method and lumped mass method, respectively. Furthermore, we establish error estimates that are associated with the noise level, iteration step, regularization parameter, and spatial discretization parameter. Finally, we present several numerical experiments in both one-dimensional and two-dimensional cases to validate the theoretical results and demonstrate the effectiveness of our proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An alternating approach for reconstructing the initial value and source term in a time-fractional diffusion-wave equation Zhang, Yun Feng, Xiaoli Yan, Xiongbin Numerical Analysis This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem by leveraging the asymptotic expansion of Mittag-Leffler functions. Subsequently, we decompose the inverse problem into two subproblems and introduce an alternating iteration reconstruction method, complemented by a regularization strategy. Additionally, a comprehensive convergence analysis for this method is provided. To solve the inverse problem numerically, we introduce two semidiscrete schemes based on standard Galerkin method and lumped mass method, respectively. Furthermore, we establish error estimates that are associated with the noise level, iteration step, regularization parameter, and spatial discretization parameter. Finally, we present several numerical experiments in both one-dimensional and two-dimensional cases to validate the theoretical results and demonstrate the effectiveness of our proposed method. |
| title | An alternating approach for reconstructing the initial value and source term in a time-fractional diffusion-wave equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.16453 |