TY - JOUR
T1 - Numerical Investigation of the Decay Rate of Solutions to Models for Water Waves with Nonlocal Viscosity
AU - S. Dumont & J.-B. Duval
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 333
EP - 349
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/571.html
KW - waterwaves, viscous asymptotical models, long-time asymptotics, fractional derivatives.
AB - <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>