In this note we show that all small solutions of the BBM equation must decay to zero as t → +∞ in large portions of the physical space, extending previous known results, and only assuming data in the energy space. Our results also include decay on the left portion of the physical line, unlike the standard KdV dynamics.
|Title of host publication||Fields Institute Communications|
|Number of pages||15|
|State||Published - 2019|
|Name||Fields Institute Communications|
Bibliographical noteFunding Information:
We thank F. Rousset and M. A. Alejo for many interesting discussions on this subject and the BBM equation. C. K. is supported by FONDECYT Postdoctorado 2017 Proyect N?3170067. C. M. work was partly funded by Chilean research grants FONDECYT1150202, Fondo Basal CMM-Chile, MathAmSud EEQUADD and Millennium Nucleus Center for Analysis of PDE NC130017. Part of this work was carried out while the authors were part of the Focus Program on Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (August 2017) held at Fields Institute, Canada. They would like to thank the Institute and the organizers for their warming support.
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