论文标题
关于分数korteweg-de vries方程的加权空间中的持久性能
On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation
论文作者
论文摘要
已经研究了涉及非本地操作员的不同色散模型的加权空间中的持久性问题。通常，这些模型不会传播任意幅度的多项式权重，并且最大衰减速率与方程式的分散部分有关。总的来说，这种分析得到了确定最佳空间衰减的独特延续原理的补充。这项工作旨在建立上述问题，以使Inviscid Burgers方程的弱色散扰动。更确切地说，我们考虑了分数Korteweg-de Vries方程，该方程包括汉堡 - hilbert方程和比本杰明 - 偏方方程弱的分散效应。
Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is associated with the dispersive part of the equation. Altogether, this analysis is complemented by unique continuation principles that determine optimal spatial decay. This work is intended to establish the above questions for a weakly dispersive perturbation of the inviscid Burgers equation. More precisely, we consider the fractional Korteweg-de Vries equation, which comprises the Burgers-Hilbert equation and dispersive effects weaker than those of the Benjamin-ono equation.
