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| Initial Boundary Value Problem for One Class of System of Multi- Dimensional Inhomogeneous GBBM Equations |
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Citation： |
Guo Boling.Initial Boundary Value Problem for One Class of System of Multi- Dimensional Inhomogeneous GBBM Equations[J].Chinese Annals of Mathematics B,1987,8(2):226~238 |
| Page view： 981
Net amount： 895 |
Authors： |
Guo Boling; |
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| Abstract： |
This paper studies the following initial-boundary value problem for the system of multidimensional inhomogeneous GBBM equations
$[\begin{array}{l}
{u_r} - \Delta {u_i} + \sum\limits_{i = 1}^n {\frac{\partial }{{\partial {x_i}}}} grad\varphi (u) = f(u),{\rm{ (1}}{\rm{.1)}}\u{|_{t = 0}} = {u_0}(x),x \in \Omega ,{\rm{ (1}}{\rm{.2)}}\u{|_{\partial \Omega }} = 0,t \ge 0,{\rm{ (1}}{\rm{.3)}}
\end{array}\]$
The existence and uniqueness of the global solution for the problem(l.l) (1.2) (1.3) are proved. The asymptotic behavior and “blow up” phenomenon of the solution for the problem (1.1) (1.2) (1.3) are investigated under certain conditions. |
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