Uniqueness properties of solutions to the Benjamin-Ono equation and related models

We prove that if u1,u2 are real solutions of the Benjamin-Ono equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono type in both the initial value problem and the initial periodic boundary...

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Detalles Bibliográficos
Autores: Kenig, C. E., Ponce, G., Vega, L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1347
Acceso en línea:http://hdl.handle.net/20.500.11824/1347
Access Level:acceso abierto
Palabra clave:Benjamin-Ono equation
Unique continuation
Descripción
Sumario:We prove that if u1,u2 are real solutions of the Benjamin-Ono equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono type in both the initial value problem and the initial periodic boundary value problem. This class of 1-dimensional non-local models includes the intermediate long wave equation. We relate our uniqueness results with those for a water wave problem. Finally, we present a slightly stronger version of our uniqueness results for the Benjamin-Ono equation.