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Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

Abstract : Abstract In this paper, we study the following water wave model with a nonlocal viscous term: u_{t}+u_{x}+\beta u_{xxx}+\frac{\sqrt{\nu}}{\sqrt{\pi}}\frac{\partial}{% \partial t}\int_{0}^{t}\frac{u(s)}{\sqrt{t-s}}\,ds+uu_{x}=\nu u_{xx}, where {\frac{1}{\sqrt{\pi}}\frac{\partial}{\partial t}\int_{0}^{t}\frac{u(s)}{\sqrt{% t-s}}\,ds} is the Riemann–Liouville half-order derivative. We prove the well-posedness of this model using diffusive realization of the half-order derivative, and we discuss the asymptotic convergence of the solution. Also, we compare our mathematical results with those given in [5] and [14] for similar equations.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03847411
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Soumis le : jeudi 10 novembre 2022 - 15:36:52
Dernière modification le : vendredi 11 novembre 2022 - 03:17:24

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Olivier Goubet, Imen Manoubi. Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach. Advances in Nonlinear Analysis, 2017, 8 (1), pp.253-266. ⟨10.1515/anona-2016-0274⟩. ⟨hal-03847411⟩

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