Global existence, traveling wave solutions and Hopf bifurcation analysis in a flame propagation model with nonlinear diffusion and advection

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-26 DOI:10.1016/j.cnsns.2025.108862

Saeed ur Rahman , José Luis Díaz Palencia , Hira Tanoli

引用次数: 0

Abstract

This paper investigates the mathematical modeling of flame propagation in porous media through a system of partial differential equations incorporating nonlinear diffusion and advection terms. We propose an extended model based on previous studies, incorporating a bistable nonlinearity and examining its behavior under various conditions. The focus is on the existence, uniqueness, and global stability of traveling wave solutions, as well as a detailed Hopf bifurcation analysis to determine the stability of equilibrium points. Using Geometric Perturbation Theory, we analyze the system’s dynamics and derive conditions for the regular convergence of traveling wave solutions.

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具有非线性扩散和平流的火焰传播模型的整体存在性、行波解和Hopf分岔分析

本文通过包含非线性扩散和平流项的偏微分方程组研究了火焰在多孔介质中传播的数学模型。我们在先前研究的基础上提出了一个扩展模型，纳入了双稳态非线性并研究了其在各种条件下的行为。重点讨论了行波解的存在性、唯一性和全局稳定性，并进行了详细的Hopf分岔分析，以确定平衡点的稳定性。利用几何摄动理论，分析了系统的动力学特性，导出了行波解正则收敛的条件。

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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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.