植被-降雨-林火相互作用模型的扭曲梯度流方法

中文摘要 AI 辅助

我们研究由两个偏微分方程（描述林火强度和水分可用性的演化）与一个常微分方程（控制植被密度）组成的植被-降雨-林火相互作用模型。该模型的主要特征是，常微分方程中存在一个乘以植被密度的非局部系数，这使得数学分析极具挑战性。本文中，我们将该非局部系数视为基础实希尔伯特空间度量结构形变的生成元，该解释使我们能将该常微分方程表述为状态依赖希尔伯特空间上的扭曲梯度流，并建立相关初边值问题强解的存在性。

英文摘要

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.

发表机构

• Institute of Electrical and Electronic Engineering, University of Boumerdes（布米尔达斯大学电气与电子工程学院）

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