Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Boudjeriou, Tahir, Ito, Akio
Institution: University of Boumerdes
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
SDG: Life on land
Open Access status: green
OpenAlex ID: W7208779113
Cites:
Cited by:
Related to: