半无限圆柱体中半线性抛物线型问题不同的渐近估计  

Asymptotic and Other Estimates for a Semilinear Parabolic Problem in a Semi-Infinite Cylinder

作　　者：J·C·宋 黄雅意(译) 张禄坤(校) 

机构地区：[1]汉阳大学应用数学系,安山京畿道426-791,韩国 [2]不详

出　　处：《应用数学和力学》2011年第10期1241-1246,共6页Applied Mathematics and Mechanics

基　　金：韩国国家研究基金会资助项目(NRF2010-0012215)

摘　　要：就变截面的半无限圆柱体,当横向边界值为0时,研究半线性抛物线型方程的初边值问题解的空间衰减.对其解的一个L2p横截面量,导出的2阶微分不等式表明,空间衰减呈O(exp{-z2/[4(t+t0)]}).同时导出了引起增长或衰减的1阶微分不等式.在爆破空间中得到增长情况下的上界,当衰减情况时,根据已知的数据,得到总能量的上界.The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries was investigated. A second-order differential inequality that was to show the spatial decay 0 （ exp { - x2 / [ 4 （ t ＋ to ） ] } ） for an L2p cross-sectional measure of the solu- tion was obtained. A first-order differential inequality leading to growth or decay was derived. In the case of growth an upper bound for blow-up in space was obtained while in the case of decay an upper bound for the total energy in terms of data was obtained.

关 键 词：空间衰减界 微分不等式 衰减率 

分 类 号：O357.1[理学—流体力学]