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Journal Articles Advances in Pure and Applied Mathematics Year : 2014

Comparison of solutions of Boussinesq systems

Abstract

We compare the solution of the generalized Boussinesq systems, for various values of a,b,c,d, \begin{eqnarray}\nonumber \eta_t +u_x +\varepsilon ((\eta u)_x +au_{xxx}-b\eta_{xxt}) &=& 0 \\\nonumber u_t +\eta_x +\varepsilon (uu_x +c\eta_{xxx} -du_{xxt}) &=&0.\end{eqnarray}These systems describe the two-way propagation of small amplitude long waves in shallow water. We prove, using an energy method introduced by Bona, Pritchard and Scott, that respective solutions of Boussinesq systems, starting from the same initial datum, remain close on a time interval inversely proportional to the wave amplitude.
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Dates and versions

hal-01090296 , version 1 (03-12-2014)

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Youcef Mammeri, Yumeng Zhang. Comparison of solutions of Boussinesq systems. Advances in Pure and Applied Mathematics, 2014, 5 (2), pp.101-115. ⟨10.1515/apam-2014-0013⟩. ⟨hal-01090296⟩
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