强迫费希尔-KPP方程的移动奇点:渐近方法

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Markus Kaczvinszki, Stefan Braun
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引用次数: 0

摘要

SIAM 应用数学杂志》第 84 卷第 2 期第 710-731 页,2024 年 4 月。 摘要发夹涡或λ涡的产生是各种边界层流动中层流-湍流过渡过程早期阶段的典型现象,在某种意义上可能与 Fisher-Kolmogorov-Petrovsky-Piskunov 方程的炸裂解有关。与这种反应扩散型非线性演化方程的通常应用不同,本课题中的解量既不需要保持有界,也不需要保持正值。我们的重点是有限时间点炸裂事件之后的解行为,它由两个向相反方向传播的移动奇点(代表涡旋腿的核心)组成,它们的初始运动通过匹配渐近展开法确定。在解决了有关渐近层的对数和代数展开项之间过渡的微妙问题后,我们发现内部奇点结构类似于二阶极点和一阶极点的组合,其形式为奇点行波,其速度随时间变化,并通过前一个炸毁事件的特征留下了印记。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Moving Singularities of the Forced Fisher–KPP Equation: An Asymptotic Approach
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 710-731, April 2024.
Abstract. The creation of hairpin or lambda vortices, typical for the early stages of the laminar-turbulent transition process in various boundary layer flows, in some sense may be associated with blow-up solutions of the Fisher–Kolmogorov–Petrovsky–Piskunov equation. In contrast to the usual applications of this nonlinear evolution equation of the reaction-diffusion type, the solution quantity in the present context needs to stay neither bounded nor positive. We focus on the solution behavior beyond a finite-time point blow-up event, which consists of two moving singularities (representing the cores of the vortex legs) propagating in opposite directions, and their initial motion is determined with the method of matched asymptotic expansions. After resolving subtleties concerning the transition between logarithmic and algebraic expansion terms regarding asymptotic layers, we find that the internal singularity structure resembles a combination of second- and first-order poles in the form of a singular traveling wave with a time-dependent speed imprinted through the characteristics of the preceding blow-up event.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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