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PreprintCC BY-NC-SA 4.0arXiv

Bottom-boundary identification using asymptotic observers in dispersive shallow-water models

  • Vishal Neeraje
  • Vishal Vasan
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Abstract

In this paper we consider the problem of identifying the bottom-boundary of an ocean basin, particularly in the coastal region where shallow-water theory applies. In particular we develop an observer-based approach of identifying the bottom-boundary profile from measurements of the free-surface. In particular, we prove that the true profile can be obtained by minimising the long-time observation-error as computed from the observer equations associated with a class of linear dispersive shallow water-wave models. We provide an explicit easy-to-implement observer design guaranteeing convergence. Numerical simulations indicate the same optimisation problem can recover the true profile for the nonlinear versions of same dispersive water-wave models.

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Cite

BibTeXRIS
BibTeX
@misc{neeraje2026bottomboundary,
  title = {{Bottom-boundary identification using asymptotic observers in dispersive shallow-water models}},
  author = {Vishal Neeraje and Vishal Vasan},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01738},
  eprint = {2611.01738},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01738},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Bottom-boundary identification using asymptotic observers in dispersive shallow-water models
AU  - Vishal Neeraje
AU  - Vishal Vasan
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01738
UR  - https://arxiv.org/abs/2611.01738
AB  - In this paper we consider the problem of identifying the bottom-boundary of an ocean basin, particularly in the coastal region where shallow-water theory applies. In particular we develop an observer-based approach of identifying the bottom-boundary profile from measurements of the free-surface. In particular, we prove that the true profile can be obtained by minimising the long-time observation-error as computed from the observer equations associated with a class of linear dispersive shallow water-wave models. We provide an explicit easy-to-implement observer design guaranteeing convergence. Numerical simulations indicate the same optimisation problem can recover the true profile for the nonlinear versions of same dispersive water-wave models.
ER  -