Wave-breaking criteria and persistence properties for the nonlocal Whitham-type equations

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-20 DOI:10.1016/j.cnsns.2025.109348

Xiaofang Dong

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引用次数: 0

Abstract

In this paper, we mainly study some nonlocal Whitham-type equations which include the

b

-family equation, the generalized rod equation and hyperelastic rod equation, the generalized Fornberg-Whitham equation and two-component Fornberg-Whitham system. A class of priori estimates of

L^{\infty}

-norm of the solution

u

to the corresponding equations is firstly constructed by making good use of the Osgood inequality. Then, based on this fact, some new wave-breaking criteria of the solutions for the equations which involve the

b

-family equation, the generalized rod equation, the hyperelastic rod equation and the generalized Fornberg-Whitham equation are obtained without the help of any conservation law properties. Finally, by the aid of the

L^{1}

-norm conservation of

ρ

and the

L^{2}

-norm of

u

with respect to a linear function of time

t

, we consider the local-in-space wave-breaking criterion of the solution for the two-component Fornberg-Whitham system by the characteristics line method. Moreover, the persistence properties of the solutions for the two-component Fornberg-Whitham system in weighted

L^{p} (R)

spaces are also investigated.

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非局部whitham型方程的破波准则和持久性

本文主要研究了b族方程、广义棒方程和超弹性棒方程、广义Fornberg-Whitham方程和双分量Fornberg-Whitham系统等非局部whitham型方程。首先利用Osgood不等式构造了相应方程解u的L∞范数的一类先验估计。在此基础上，得到了b族方程、广义棒方程、超弹性棒方程和广义Fornberg-Whitham方程解的一些新的破波判据，而不借助于任何守恒律性质。最后，利用ρ的l1范数守恒和u对时间为t的线性函数的l2范数守恒，用特征线法考虑了双分量Fornberg-Whitham系统解的空间局部破波判据。此外，还研究了两分量Fornberg-Whitham系统在加权Lp(R)空间中解的持续性。

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.