论文标题
用于与立方非线性的分散性方程的凯基问题解决方案的渐近渐近概况
Higher-order asymptotic profiles for solutions to the Cauchy problem for a dispersive-dissipative equation with a cubic nonlinearity
论文作者
论文摘要
我们考虑解决方案的cauchy问题的渐近行为，用于具有立方非线性的分散性方程。众所周知，解决该问题的解决方案的渐近概况的主要项是高斯。此外，通过分析相应的积分方程，已经获得了对线性部分解决方案的高阶渐近扩展，并且已经获得了Duhamel项的第一个渐近谱。在本文中，我们为Duhamel术语构建了第二个渐近曲线，并为溶液的更详细的高阶渐近扩展提供了概括，从而概括了先前的作品。此外，我们强调，新获得的高阶渐近轮廓在满足抛物线寄生虫自相似性的意义上具有良好的结构。
We consider the asymptotic behavior of solutions to the Cauchy problem for a dispersive-dissipative equation with a cubic nonlinearity. It is known that the leading term of the asymptotic profile for the solution to this problem is the Gaussian. Moreover, by analyzing the corresponding integral equation, the higher-order asymptotic expansion for the solution to the linear part and the first asymptotic profile for the Duhamel term have already been obtained. In this paper, we construct the second asymptotic profile for the Duhamel term and give the more detailed higher-order asymptotic expansion of the solutions, which generalizes the previous works. Furthermore, we emphasize that the newly obtained higher-order asymptotic profiles have a good structure in the sense of satisfying the parabolic self-similarity.
