Abstract
In this article, we study the initial value problem associated with a five-parameter Boussinesq-type system. We prove local existence and uniqueness of the solution and that the supremum norm of the solution decays algebraically to zero as ( 1 + t ) − 1 / 3 when t approaches to infinity, provided the initial data are sufficiently small and regular. We further present a high-accurate spectral numerical method to approximate the solutions and validate the theoretical results.
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