@Article{IJNAM-10-333,
author = {S. Dumont and J.-B. Duval},
title = {Numerical Investigation of the Decay Rate of Solutions to Models for Water Waves with Nonlocal Viscosity},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {2},
pages = {333--349},
abstract = {<p style="text-align: justify;">In this article, we investigate the decay rate of the solutions of two water wave models
with a nonlocal viscous term written in the KdV form $$u_t+u_x+\beta u_{xxx}+\frac{\sqrt v}{\sqrt \pi}\int^t_0\frac{u_t(s)}{\sqrt{t-s}}ds+uu_x=vu_{xx}$$ and $$u_t+u_x-\beta u_{txx}+\frac{\sqrt v}{\sqrt \pi}\int^t_0\frac{u_t(s)}{\sqrt{t-s}}ds+uu_x=vu_{xx}$$ in the BBM form. In order to realize this numerical study, a numerical scheme based on the $G^{\alpha}$-scheme is developed.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/571.html}
}