TY - JOUR
T1 - Global <em>W</em><sup>2,<em>p</em></sup> Solutions of GBBM Equations on Unbounded Domain
AU - Haiping Mo & Yacheng Liu 
JO - Journal of Partial Differential Equations
VL - 4
SP - 349
EP - 355
PY - 2001
DA - 2001/11
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5488.html
KW - GBBM equation
KW - unbounded domain
KW - global W^{2
KW - p} solutions
KW - existence
AB -  In this paper we study the initial boundary value problem of GBBM equations on unbounded domain u_t - Δu_t = div f(u) u(x,0) = u_0(x) u|_{∂Ω} = 0 and corresponding Cauchy problem. Under the conditions: f( s) ∈ C^sup1 and satisfies (H)\qquad |f&#39;(s)| ≤ C|s|^ϒ, 0 ≤ ϒ ≤ \frac{2}{n-2} if n ≥ 3; 0 ≤ ϒ &lt; ∞ if n = 2 u_0(x) ∈ W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω)(W^{2,p}(R^n) ∩ W^{2,2}(R^n) for Cauchy problem), 2 ≤ p &lt; ∞, we obtain the existence and uniqueness of global solution u(x, t) ∈ W^{1,∞}(0, T; W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω))(W^{1,∞}(0, T; W^{2,p}(R^n) ∩ W^{2,2} (R^n)) for Cauchy problem), so the results of [1] and [2] are generalized and improved in essential.