论文标题
大量的时间行为和最佳衰减估计值，用于2D中的广义kadomtsev--petviashvili-burgers方程
Large time behavior and optimal decay estimate for solutions to the generalized Kadomtsev--Petviashvili--Burgers equation in 2D
论文作者
论文摘要
我们考虑了2D中广义的kadomtsev--petviashvili-burgers方程的库奇问题。这是非线性分散型型方程之一，具有空间各向异性耗散术语。在初始数据$ u_ {0} $上的一些适当的规律性假设下，尤其是条件$ \ partial_ {x}^{ - 1} u_ {0} \ in l^{1}（\ Mathbb {r}^{2}）$，已知该问题以$ t}的速度降临。在$ l^{\ infty} $ - sense中。在本文中，我们研究了解决方案的更详细的大时间行为，并在$ t \ to \ infty $上构建解决方案的近似公式。此外，我们获得了解决方案的$ l^{\ infty} $的下限，并证明了衰减速率$ t^{ - \ frac {7} {4}}} $是以前工作中给出的解决方案的最佳解决方案。
We consider the Cauchy problem for the generalized Kadomtsev--Petviashvili--Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a spatial anisotropic dissipative term. Under some suitable regularity assumptions on the initial data $u_{0}$, especially the condition $\partial_{x}^{-1}u_{0} \in L^{1}(\mathbb{R}^{2})$, it is known that the solution to this problem decays at the rate of $t^{-\frac{7}{4}}$ in the $L^{\infty}$-sense. In this paper, we investigate the more detailed large time behavior of the solution and construct the approximate formula for the solution at $t\to \infty$. Moreover, we obtain a lower bound of the $L^{\infty}$-norm of the solution and prove that the decay rate $t^{-\frac{7}{4}}$ of the solution given in the previous work to be optimal.
