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,
{utt−uxx+(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 s≥0 with the initial data φ, ψ lie in Hs(0,1) and Hs−2(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(s−1)/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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Wellposedness of the sixth order Boussinesq equation with non-homogeneous boundary values on a bounded domain
Li, Shenghao
Chen, Min
Zhang, Bingyu
Physica D: Nonlinear Phenomena, Vol. 389 (2019), Iss. P.13
https://doi.org/10.1016/j.physd.2018.09.006 [Citations: 6]