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arXiv · 1901.11432

Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models

Carlos E. Kenig·Gustavo Ponce·Luis Vega
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Abstract

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.

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Carlos E. Kenig, Gustavo Ponce, Luis Vega. 2019-01-31. Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models. https://arxiv.org/abs/1901.11432

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