Existence and asymptotic decay for a Boussinesq-type model

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• 作者：Juan Carlos Muñ ; oz Grajales ; Ivonne Rivas Triviñ ; o
• 关键词：Asymptotic decay ; Cauchy problem ; Spectral methods ; Fourier transform
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 September 2008
• 年：2008
• 卷：345
• 期：1
• 页码：455-475
• 全文大小：761 K

文摘

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.