对一类具有不连续右手边和多根退化解的奇异扰动系统的多尺度研究

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-07 DOI:10.1016/j.cnsns.2024.108247

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引用次数: 0

摘要

研究了具有双根退化方程的奇异扰动系统的两点边界值问题。这是一类新问题，当系统右端的非线性项在直线上不连续时，会形成复杂的多区域内层，在不连续直线附近可分为八个区域。本文不仅利用修正边界层函数法得到了平滑解，还利用匹配法证明了问题解的存在性。并给出了其余量估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Multiscale study on a class of singularly perturbed system with discontinuous right-hand side and multiple root of the degenerate solution

A two point boundary value problem for a singularly perturbed system with double root of the degenerate equation is studied. This is a new class of problem in the case when the nonlinear term at the right end of the system is discontinuous on the straight line, which leads to the formation of complex multizonal internal layers that can be divided into eight regions in the neighborhood of the discontinuous straight line. In this paper, not only the modified boundary layer function method is used to obtain a smooth solution, but also the matching method is used to prove the existence of the solution to the problem. And its remainder estimation is given.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.