# Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Considerations

## 3. Conditions for Bounded Solutions

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

## 4. Existence of Absorbing Sets

**Theorem**

**2.**

**Proof.**

**Remark**

**3.**

## 5. Results and Implications

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**On the left: the bounded solution u(t) when $\epsilon \beta =3.6,$ ${u}_{0}=1$, ${C}_{1}=-0.2,$ ${C}_{2}=0.2.$ On the right: the bounded functions $u\left(t\right)$ as $-0.6\le {C}_{1}\le 0.2$.

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De Angelis, M.
Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets. *Mathematics* **2022**, *10*, 2041.
https://doi.org/10.3390/math10122041

**AMA Style**

De Angelis M.
Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets. *Mathematics*. 2022; 10(12):2041.
https://doi.org/10.3390/math10122041

**Chicago/Turabian Style**

De Angelis, Monica.
2022. "Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets" *Mathematics* 10, no. 12: 2041.
https://doi.org/10.3390/math10122041