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A Nonhomogeneous Boundary Value Problem for the Boussinesq Equation on a Bounded Domain

A Nonhomogeneous Boundary Value Problem for the Boussinesq Equation on a Bounded Domain

Year:    2016

Author:    Sheng-Hao Li, Ivonne Rivas, Bing-Yu Zhang

Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 238–258

Abstract

In this paper, we study the well-posedness of an initial-boundary-value problem (IBVP) for the Boussinesq equation on a bounded domain,

{uttuxx+(u2)xx+uxxxx=0,x(0,1),t>0,u(x,0)=φ(x),ut(x,0)=ψ(x),u(0,t)=h1(t),u(1,t)=h2(t),uxx(0,t)=h3(t),uxx(1,t)=h4(t). It is shown that the IBVP is locally well-posed in the space Hs(0,1) for any s0 with the initial data φ, ψ lie in Hs(0,1) and Hs2(0,1), respectively, and the naturally compatible boundary data h1, h2 in the space H(s+1)/2loc(R+), and h3, h4 in the the space of H(s1)/2loc(R+) with optimal regularity.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v49n3.16.03

Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 238–258

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Boussinesq equation initial-boundary value problem local well-posedness.

Author Details

Sheng-Hao Li Email

Ivonne Rivas Email

Bing-Yu Zhang Email

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