奇异点和时间噪声支配的非线性偏微分方程的存在性理论和精确解

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2023-01-09 DOI:10.15388/namc.2023.28.30563

M. O. Ahmed, R. Naeem, Muhammad Akhtar Tarar, M. S. Iqbal, M. Inc., Farkhanda Afzal

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引用次数: 2

摘要

目前的研究涉及具有两个重要困难的非线性偏微分方程的精确解，即系数奇异性和随机函数（白噪声）。当代研究有四大贡献。一种是数学分析，其中解存在性的显式先验估计是由Schauder不动点定理构造的。其次，当奇异参数为→ 第三，微分方程中存在的噪声的影响已经在精确解中得到了成功的处理。最后的贡献是模拟精确的解决方案并解释绘图。

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Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise

The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.