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Neural Processing Letters
Erschienen in: Neural Processing Letters 5/2021

10.06.2021

Existence, Uniqueness and Stability of Mild Solutions to a Stochastic Nonlocal Delayed Reaction–Diffusion Equation

verfasst von: Wenjie Hu, Quanxin Zhu

Erschienen in: Neural Processing Letters | Ausgabe 5/2021

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Abstract

The aim of this paper is to investigate the existence, uniqueness and stability of mild solutions to a stochastic delayed reaction–diffusion equation with spatial non-locality. This equation can be used to model the spatial–temporal evolution for age-structured spices perturbed by some random effects or the stochastic neural networks. The Banach fixed point theorem and a truncation method are adopted to establish the existence and uniqueness of mild solutions under both global and local Lipschitz conditions. Then, we explore the mean square exponential stability and almost sure exponential stability by employing the inequality techniques, the stochastic analysis techniques together with the properties of the nonlocal delayed term. Furthermore, we obtain the critical value of time delay \(\tau \) that guarantees the stability of the mild solutions. At last, our theoretic results are illustrated by application to the stochastic non-local delayed Nicholson blowflies equation with numerical simulations.
Vorheriger Artikel Jacobi Neural Network Method for Solving Linear Differential-Algebraic Equations with Variable Coefficients
Nächster Artikel Interval Neutrosophic Einstein Prioritized Normalized Weighted Geometric Bonferroni Mean Operator and its Application to Multicriteria Decision making

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Metadaten
Titel
Existence, Uniqueness and Stability of Mild Solutions to a Stochastic Nonlocal Delayed Reaction–Diffusion Equation
verfasst von
Wenjie Hu
Quanxin Zhu
Publikationsdatum
10.06.2021
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 5/2021
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-021-10559-x

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