一类偏泛函微分方程的测度伪型解及在生物数学模型中的应用
A Class of Measure Pseudo Type Solution of Partial Functional Differential Equations and Applications in Biomathematical Model
DOI: 10.12677/AAM.2023.125250, PDF, HTML, 下载: 156  浏览: 225 
作者: 王芳：浙江长征职业技术学院基础部，浙江 杭州
关键词: 偏泛函微分方程；无穷时滞；测度论；分数幕算子；Partial Functional Differential Equations； Infinite Delay； Measure Theory； Fractional Power of Operators
摘要: 本文研究了一类具有无限时滞的α-型偏泛函微分方程测度伪型解的存在性和唯一性。 文中假设线 性算子部分在Banach 空间X 上生成紧的解析半群，然后利用分数幕算子理论和算子半群理论证明了方程解的存在唯一性，并将其应用于一类生物数学模型中，验证结论的正确性。
Abstract: In this paper, the existence, uniqueness of measure pseudo type solutions in the α-form for partial functional differential equations with infinite delay are investigated. Here we assume that the linear part generates a compact analytic semigroup on a Banach space X, the delayed part is assumed to be continuous with respect to the fractional power of the generator. Finally, an example of biomathematical model is presented to illustrate the main findings.
文章引用：王芳. 一类偏泛函微分方程的测度伪型解及在生物数学模型中的应用[J]. 应用数学进展, 2023, 12(5): 2480-2492. https://doi.org/10.12677/AAM.2023.125250

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