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PreprintCC BY 4.0arXiv

Twisted Gradient Flow Approach to Vegetation-Rainfall-Bushfire Interactions Model

  • Tahir Boudjeriou
  • Akio Ito
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Abstract

We consider a vegetation-rainfall-bushfire interaction model consisting of two partial differential equations describing the evolutions of bushfire intensity and water availability, together with an ordinary differential equation governing the vegetation density. The main feature of the model is that the ODE contains a nonlocal coefficient multiplying the vegetation density, which makes the mathematical analysis highly nontrivial. In this paper, we regard this nonlocal coefficient as the generator of a deformation of the metric structure of the underlying real Hilbert space. This interpretation enables us to formulate the ODE as a twisted gradient flow on state-dependent Hilbert spaces and to establish the existence of strong solutions to the associated initial-boundary value problem.

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Cite

BibTeXRIS
BibTeX
@misc{boudjeriou2026twisted,
  title = {{Twisted Gradient Flow Approach to Vegetation-Rainfall-Bushfire Interactions Model}},
  author = {Tahir Boudjeriou and Akio Ito},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03386},
  eprint = {2609.03386},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03386},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Twisted Gradient Flow Approach to Vegetation-Rainfall-Bushfire Interactions Model
AU  - Tahir Boudjeriou
AU  - Akio Ito
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03386
UR  - https://arxiv.org/abs/2609.03386
AB  - We consider a vegetation-rainfall-bushfire interaction model consisting of two partial differential equations describing the evolutions of bushfire intensity and water availability, together with an ordinary differential equation governing the vegetation density. The main feature of the model is that the ODE contains a nonlocal coefficient multiplying the vegetation density, which makes the mathematical analysis highly nontrivial. In this paper, we regard this nonlocal coefficient as the generator of a deformation of the metric structure of the underlying real Hilbert space. This interpretation enables us to formulate the ODE as a twisted gradient flow on state-dependent Hilbert spaces and to establish the existence of strong solutions to the associated initial-boundary value problem.
ER  -