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Neutral Functional Differential Equations with Applications to Compartmental Systems

Víctor Muñoz-Villarragut, Sylvia Novo, Rafael Obaya

TL;DR

The stability properties of D allow us to introduce a new order and to take the neutral family to a family of functional differential equations with infinite delay and the 1-covering property of omega-limit sets under the componentwise separating property and uniform stability is established.

Abstract

We study the monotone skew-product semiflow generated by a family of neutral functional differential equations with infinite delay and stable D-operator. The stability properties of D allow us to introduce a new order and to take the neutral family to a family of functional differential equations with infinite delay. Next, we establish the 1-covering property of omega-limit sets under the componentwise separating property and uniform stability. Finally, the obtained results are applied to the study of the long-term behavior of the amount of material within the compartments of a neutral compartmental system with infinite delay.

Neutral Functional Differential Equations with Applications to Compartmental Systems

TL;DR

The stability properties of D allow us to introduce a new order and to take the neutral family to a family of functional differential equations with infinite delay and the 1-covering property of omega-limit sets under the componentwise separating property and uniform stability is established.

Abstract

We study the monotone skew-product semiflow generated by a family of neutral functional differential equations with infinite delay and stable D-operator. The stability properties of D allow us to introduce a new order and to take the neutral family to a family of functional differential equations with infinite delay. Next, we establish the 1-covering property of omega-limit sets under the componentwise separating property and uniform stability. Finally, the obtained results are applied to the study of the long-term behavior of the amount of material within the compartments of a neutral compartmental system with infinite delay.
Paper Structure (6 sections, 26 theorems, 92 equations)

This paper contains 6 sections, 26 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. Some preliminaries
  3. Stable $D$-operators
  4. Monotone neutral functional differential equations
  5. Compartmental systems
  6. Long-term behavior of compartmental systems

Key Result

Proposition 3.1

\newlabelDD1D2 If $D\colon BU\to \mathbb{R}^m$ satisfies ${\rm (D1)}$ and ${\rm(D2)}$, then for each $x\in BU$ where $\mu=[\mu_{ij}]$ and $\mu_{ij}$ is a real regular Borel measure with finite total variation $|\mu_{ij}|(-\infty,0]<\infty$, for all $i$, $j\in\{1,\ldots,m\}$.

Theorems & Definitions (53)

  • Proposition 3.1
  • proof
  • Proposition 3.2
  • Lemma 3.3
  • proof
  • Definition 3.4
  • Proposition 3.5
  • proof
  • Theorem 3.6
  • proof
  • ...and 43 more