Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach
2017 ◽
Vol 8
(1)
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pp. 253-266
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Keyword(s):
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.
2010 ◽
Vol 27
(4)
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pp. 1473-1492
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2018 ◽
Vol 41
(12)
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pp. 4810-4826
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2019 ◽
Vol 20
(1)
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pp. 141-163
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Keyword(s):
2014 ◽
Vol 19
(9)
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pp. 2837-2863
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Keyword(s):
2014 ◽
Vol 38
(19-20)
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pp. 4912-4925
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2020 ◽
Vol 148
(12)
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pp. 5181-5191
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