On the unique continuation of solutions to non-local non-linear dispersive equations
| Autor: | Carlos E. Kenig, Luis Vega, Didier Pilod, Gustavo Ponce |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Large class
35Q55 35B05 Nonlinear dispersive equation non-local operators Applied Mathematics 010102 general mathematics Mathematics::Classical Analysis and ODEs Mathematics::Analysis of PDEs Mathematics::General Topology Non local 01 natural sciences 010101 applied mathematics Nonlinear system Continuation Mathematics - Analysis of PDEs FOS: Mathematics Applied mathematics 0101 mathematics Analysis Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Partial Differential Equations |
| Popis: | 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 $\Omega\subset \mathbb R^n\times[0,T]$, $u_1(x,t)=u_2(x,t)$ for $(x,t) \in \Omega$, 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. Comment: 18 pages |
| Databáze: | OpenAIRE |
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