On the unique continuation of solutions to non-local non-linear dispersive equations

被引：16

作者：

Kenig, C. E. ^{[1
]}

Pilod, D. ^{[2
]}

Ponce, G. ^{[3
]}

Vega, L. ^{[4
,5
]}

机构：

[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[2] Univ Bergen, Dept Math, Postbox 7800, N-5020 Bergen, Norway

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

[4] Univ Basque Country, Dept Matemat, Bilbao, Spain

[5] Basque Ctr Appl Math, Bilbao, Spain

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 45卷 / 08期

关键词：

Nonlinear dispersive equation; non-local operators; FRACTIONAL SCHRODINGER-EQUATIONS; WELL-POSEDNESS; BENJAMIN-ONO; SOLITARY WAVES; BURGERS; PERTURBATIONS; DYNAMICS;

D O I：

10.1080/03605302.2020.1739707

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if are two suitable solutions of the equation defined in such that for some non-empty open set for then for any The proof is based on static arguments. More precisely, the main ingredient in the proofs will be the unique continuation properties for fractional powers of the Laplacian established by Ghosh, Salo and Ulhmann, and some extensions obtained here.

引用

页码：872 / 886

页数：15

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