以分数幂级数表示的分数平流-分散方程的解的存在性和唯一性

Symmetry Pub Date : 2024-09-02 DOI:10.3390/sym16091137
Alexandru-Nicolae Dimache, Ghiocel Groza, Marilena Jianu, Iulian Iancu
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引用次数: 0

摘要

在地下水水文学中,分数平流-分散方程用于模拟多孔介质中污染物/固态颗粒随流动地下水以渗流速度的运动。该模型用于预测非反应性溶解污染物在地下水中的迁移。本文确定了分数平流-扩散方程的一些初值问题和边界值问题的分数双变量幂级数解的存在性和唯一性。此外,还设计了一种使用双变量分数多项式近似求解的方法,以及在合适的矩形范围内评估误差的方法。此外,还介绍了显示理论结果适用性的示例。
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Existence and Uniqueness of Solution Represented as Fractional Power Series for the Fractional Advection–Dispersion Equation
The fractional advection–dispersion equation is used in groundwater hydrology for modeling the movements of contaminants/solute particles along with flowing groundwater at the seepage velocity in porous media. This model is used for the prediction of the transport of nonreactive dissolved contaminants in groundwater. This paper establishes the existence and the uniqueness of solutions represented as fractional bi-variate power series of some initial-value problems and boundary-value problems for the fractional advection–dispersion equation. Moreover, a method to approximate the solutions using fractional polynomials in two variables and to evaluate the errors in a suitable rectangle is designed. Illustrative examples showing the applicability of the theoretical results are presented.
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