On decay of the solutions for the dispersion generalized Benjamin--Ono and Benjamin--Ono equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-05 DOI:10.57262/ade027-1112-781

Alysson Cunha

引用次数: 1

Abstract

. We show that uniqueness results of the kind those obtained for KdV and Schr¨odinger equations ([7], [28]), are not valid for the dispersion generalized-Benjamin-Ono equation in the weighted Sobolev spaces for appropriated s and r . In particular, we obtain that the uniqueness result proved for the dispersion generalized- Benjamin-Ono equation ([13]), is not true for all pairs of solutions u 1 6 = 0 and u 2 6 = 0. To achieve these results we employ the techniques present in our recent work [6]. We also improve some Theorems established for the dispersion generalized-Benjamin-Ono equation and for the Benjamin-Ono equation ([13], [12]).

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色散广义Benjamin—Ono和Benjamin—Ono方程解的衰减

．我们证明了关于KdV和Schr¨odinger方程([7]，[28])的唯一性结果，不适用于分配s和r的加权Sobolev空间中的色散广义benjamin - ono方程。特别地，我们得到了对于弥散广义- Benjamin-Ono方程([13])所证明的唯一性结果，并不是对u 16 = 0和u 26 = 0的所有解对都成立。为了达到这些结果，我们采用了我们最近的工作[6]中的技术。我们还改进了关于色散广义Benjamin-Ono方程和Benjamin-Ono方程([13]，[12])的定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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