On Existence and Uniqueness of Positive Solutions to Population Balance Models for Column Crystallizers

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-27 DOI:10.1002/mma.70032

Elias G. Saleeby, Nima Rabiei

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引用次数: 0

Abstract

In this article, we prove the existence and uniqueness of positive/nonnegative solutions on $[0, \infty)$ of population balance models for column crystallizers. These solutions represent the crystal size distributions in the stages of the column. We first investigate a system of ODEs model for a column with no particle agglomeration. Then we consider a system of integrodifferential equations (IDEs) model that accounts for particle agglomeration. In this case, we turn a boundary value problem for a Fredholm-Volterra system of IDEs into an initial value problem of Volterra type IDEs coupled with a system of algebraic equations. We obtain our results employing some algebraic facts along with the Brouwer and the Schauder's fixed point theorems.

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塔式结晶器种群平衡模型正解的存在唯一性

本文证明了塔式结晶器种群平衡模型在[0，∞)$$ \left[0,\infty \right) $$上正/非负解的存在唯一性。这些溶液代表了柱级中晶体尺寸的分布。我们首先研究了一个无颗粒团聚柱的ODEs模型系统。然后，我们考虑了一个系统的积分微分方程（IDEs）模型，说明粒子团聚。在这种情况下，我们把一类非线性非线性方程的Fredholm-Volterra系统的边值问题转化为一个与代数方程组耦合的Volterra型非线性方程的初值问题。我们利用一些代数事实以及布劳威尔不动点定理和绍德不动点定理得到了我们的结果。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.