论文标题
粘性Fornberg-Whitham方程解决方案的高阶渐近概况
Higher-order asymptotic profiles of the solutions to the viscous Fornberg-Whitham equation
论文作者
论文摘要
我们考虑了粘性福恩伯格 - Whitham方程的初始值问题，该方程是非线性和非局部分散性分散方程之一。在本文中，我们建立了解决方案的全球存在并研究其渐近行为。我们表明，由于粘度项的耗散效应，我们表明该问题的解决方案会收敛到称为非线性扩散波的汉堡方程。此外，我们通过构建高阶渐近谱分析了非线性扩散波和溶液的详细结构的最佳渐近速率。此外，我们研究了非局部分散项如何影响解决方案的渐近行为，并将结果与KDV-燃烧器方程的结果进行比较。
We consider the initial value problem for the viscous Fornberg-Whitham equation which is one of the nonlinear and nonlocal dispersive-dissipative equations. In this paper, we establish the global existence of the solutions and study its asymptotic behavior. We show that the solution to this problem converges to the self-similar solution to the Burgers equation called the nonlinear diffusion wave, due to the dissipation effect by the viscosity term. Moreover, we analyze the optimal asymptotic rate to the nonlinear diffusion wave and the detailed structure of the solution by constructing higher-order asymptotic profiles. Also, we investigate how the nonlocal dispersion term affects the asymptotic behavior of the solutions and compare the results with the ones of the KdV-Burgers equation.
