标题： 高阶色散方程的平滑效应及其在非线性初值问题中的应用 显示英文标题

标题： Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems

摘要： 在本文中，我们研究与一类色散非均匀演化方程 Pu=f 相关的初值问题，其中变量系数属于 p-演化方程类，$p\geq 2$。 我们研究由线性算子 P 的次主导系数的虚部的空间衰减假设所产生的平滑效应。然后我们将此结果应用于具有导数非线性的非线性问题，从而在适当的 Sobolev 类中获得解的存在性和唯一性。 所考虑的非线性方程包括各种物理兴趣的方程，如 KdV 型和 Kawahara 型方程。 显示英文摘要

摘要： In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p-evolution equations, $p\geq 2$. We study the smoothing effect produced by some spatial decay assumptions on the imaginary part of the subleading coefficient of the linear operator P. Then we apply this result to nonlinear problems with derivative nonlinearities obtaining existence and uniqueness of the solution in a suitable Sobolev class. The nonlinear equations considered include various equations of physical interest such as KdV-type and Kawahara-type equations.