On the unique continuation of solutions to non-local non-linear dispersive equations
Journal article, Peer reviewed
Published version
View/ Open
Date
2020Metadata
Show full item recordCollections
- Department of Mathematics [927]
- Registrations from Cristin [9371]
Original version
Communications in Partial Differential Equations. 2020, 45 (8), 872-886. 10.1080/03605302.2020.1739707Abstract
We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if u1,u2 are two suitable solutions of the equation defined in Rn×[0,T] such that for some non-empty open set Ω⊂Rn×[0,T],u1(x,t)=u2(x,t) for (x,t)∈Ω, then u1(x,t)=u2(x,t) for any (x,t)∈Rn×[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, and some extensions obtained here.