论文标题
关于非本地非线性分散方程的独特解决方案的独特延续
On the unique continuation of solutions to non-local non-linear dispersive equations
论文作者
论文摘要
我们证明了解决方案对大型非线性，非本地分散方程的独特延续性。目的是表明，如果$ u_1，\，u_2 $是$ \ mathbb r^n \ times [0，t] $定义的两种方程解决方案，以至于对于某些非空的打开集$ subset $ subset \ subbb r^n \ times [0， $ u_1（x，t）= u_2（x，t）$ for \ in \ mathbb r^n \ times [0，t] $。证明基于静态论点。更确切地说，证明中的主要成分将是\ cite {ghsauh}建立的Laplacian分数的独特延续性能，以及此处获得的一些扩展。
We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if $u_1,\,u_2$ are two suitable solutions of the equation defined in $\mathbb R^n\times[0,T]$ such that for some non-empty open set $Ω\subset \mathbb R^n\times[0,T]$, $u_1(x,t)=u_2(x,t)$ for $(x,t) \in Ω$, then $u_1(x,t)=u_2(x,t)$ for any $(x,t)\in\mathbb R^n\times[0,T]$. 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 in \cite{GhSaUh}, and some extensions obtained here.
