论文标题
广义福nberg-Whitham方程的解决方案的渐近概况与耗散
Asymptotic profiles of solutions for the generalized Fornberg-Whitham equation with dissipation
论文作者
论文摘要
我们考虑了随着耗散的广义福nberg-whitham方程的库奇问题。这是非线性，非局部和分散性分离方程之一。本文的主要主题是针对该问题解决方案的渐近分析。我们证明，解决此问题的解决方案会收敛到修改的热核。此外，我们根据非线性程度构建解决方案的第二项。鉴于第二个渐近谱，我们研究了分散，耗散和非线性项对溶液渐近行为的影响。
We consider the Cauchy problem for the generalized Fornberg-Whitham equation with dissipation. This is one of the nonlinear, nonlocal and dispersive-dissipative equations. The main topic of this paper is an asymptotic analysis for the solutions to this problem. We prove that the solution to this problem converges to the modified heat kernel. Moreover, we construct the second term of asymptotics for the solutions depending on the degree of the nonlinearity. In view of those second asymptotic profiles, we investigate the effects of the dispersion, dissipation and nonlinear terms on the asymptotic behavior of the solutions.
