Identification of space-dependent coefficients in two competing terms of a nonlinear subdiffusion equation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910005927608320 |
|---|---|
| author | Kaltenbacher, Barbara Rundell, William |
| author_facet | Kaltenbacher, Barbara Rundell, William |
| contents | We consider a (sub)diffusion equation with a nonlinearity of the form $pf(u)-qu$, where $p$ and $q$ are space dependent functions. Prominent examples are the Fisher-KPP, the Frank-Kamenetskii-Zeldovich and the Allen-Cahn equations. We devise a fixed point scheme for reconstructing the spatially varying coefficients from interior observations a) at final time under two different excitations b) at two different time instances under a single excitation. Convergence of the scheme as well as local uniqueness of these coefficients is proven. Numerical experiments illustrate the performance of the reconstruction scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Identification of space-dependent coefficients in two competing terms of a nonlinear subdiffusion equation Kaltenbacher, Barbara Rundell, William Numerical Analysis We consider a (sub)diffusion equation with a nonlinearity of the form $pf(u)-qu$, where $p$ and $q$ are space dependent functions. Prominent examples are the Fisher-KPP, the Frank-Kamenetskii-Zeldovich and the Allen-Cahn equations. We devise a fixed point scheme for reconstructing the spatially varying coefficients from interior observations a) at final time under two different excitations b) at two different time instances under a single excitation. Convergence of the scheme as well as local uniqueness of these coefficients is proven. Numerical experiments illustrate the performance of the reconstruction scheme. |
| title | Identification of space-dependent coefficients in two competing terms of a nonlinear subdiffusion equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.21018 |