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PreprintCC BY-NC 4.0HAL

RECOVERY OF A SOURCE OF ANOMALOUS DIFFUSION FROM SPACE-TIME SPARSE DATA

  • Xing Cheng
  • Jin Bangti
  • Yavar Kian
  • Zhiyuan Li
Open at sourcePDFDOICite

Abstract

We study an inverse source problem for a time-fractional sub-and super-diffusive anomalous diffusion equation on the unit disk with sparse boundary observations. We prove the recovery of a general class of L 2 sources for anomalous diffusion, with separated variables, from boundary measurements that are sparse in both space and time, using observations at two carefully chosen boundary points on a discrete set of times arbitrarily close to the final time. The analysis relies heavily on the memory effect of the model, properties of complex analysis and the representation of solutions.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026recovery,
  title = {{RECOVERY OF A SOURCE OF ANOMALOUS DIFFUSION FROM SPACE-TIME SPARSE DATA}},
  author = {Xing Cheng and Jin Bangti and Yavar Kian and Zhiyuan Li},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33896},
  eprint = {2610.33896},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05840253v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - UNPB
TI  - RECOVERY OF A SOURCE OF ANOMALOUS DIFFUSION FROM SPACE-TIME SPARSE DATA
AU  - Xing Cheng
AU  - Jin Bangti
AU  - Yavar Kian
AU  - Zhiyuan Li
PY  - 2026
DA  - 2026/10/24
PB  - HAL
DO  - 10.48550/arxiv.2610.33896
UR  - https://hal.science/hal-05840253v1
AB  - We study an inverse source problem for a time-fractional sub-and super-diffusive anomalous diffusion equation on the unit disk with sparse boundary observations. We prove the recovery of a general class of L 2 sources for anomalous diffusion, with separated variables, from boundary measurements that are sparse in both space and time, using observations at two carefully chosen boundary points on a discrete set of times arbitrarily close to the final time. The analysis relies heavily on the memory effect of the model, properties of complex analysis and the representation of solutions.
ER  -