Uniqueness properties of solutions to the Benjamin-Ono equation and related models
Copyright policy )Uniqueness properties of solutions to the Benjamin-Ono equation and related models
We prove that if $u_1,\,u_2$ are solutions of the Benjamin-Ono equation defined in $ (x,t)\in\R \times [0,T]$ which agree in an open set $Ω\subset \R \times [0,T]$, then $u_1\equiv u_2$. 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. Finally, we present a slightly stronger version of our uniqueness results for the Benjamin-Ono equation.
- University of California, Santa Barbara United States
- UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA Spain
- University of Chicago United States
- Basque Center for Applied Mathematics Spain
- University of the Basque Country Spain
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, PDEs in connection with fluid mechanics, unique continuation, Benjamin-Ono equation, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), FOS: Mathematics, Unique continuation, Analysis of PDEs (math.AP)
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, PDEs in connection with fluid mechanics, unique continuation, Benjamin-Ono equation, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), FOS: Mathematics, Unique continuation, Analysis of PDEs (math.AP)
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