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Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2023

On the linearized Whitham–Broer–Kaup system on bounded domains

Résumé

We consider the system of partial differential equations on bounded domains, known in the literature as the Whitham–Broer–Kaup system. The well-posedness of the problem, under suitable boundary conditions, is addressed, and it is shown to depend on the sign of the number $\varkappa = \alpha-\beta^2.$ In particular, existence and uniqueness occur if and only if $\varkappa > 0$. In which case, an explicit representation for the solutions is given. Nonetheless, for the case $\varkappa \leq 0$ we have uniqueness in the class of strong solutions, and sufficient conditions to guarantee exponential instability are provided.
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Dates et versions

ujm-04347781 , version 1 (15-12-2023)

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L. Liverani, Youcef Mammeri, V. Pata, R. Quintanilla. On the linearized Whitham–Broer–Kaup system on bounded domains. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2023, pp.1-20. ⟨10.1017/prm.2023.85⟩. ⟨ujm-04347781⟩
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