A system of state-dependent delay differential equation modelling forest growth I: semiflow properties

TL;DR

This paper studies the mathematical properties of a class of state-dependent delay differential equations modeling forest growth, focusing on semiflow existence, uniqueness, blow-up behavior, and an application to spatial forest models.

Contribution

It establishes the existence and uniqueness of semiflows for these equations and analyzes blow-up phenomena, extending the mathematical understanding of forest growth models.

Findings

Proved semiflow existence and uniqueness in Lipschitz and $C^1$ spaces.

Identified conditions leading to blow-up of solutions.

Applied the theory to a spatially structured forest model.

Abstract

In this article we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the existence and uniqueness of a semiflow in the space of Lipschitz and $C^1$ weighted functions. We obtain a blow-up result when the time approaches the maximal time of existence. We conclude the paper with an application of a spatially structured forest model.