半无限圆柱体中半线性抛物线型问题不同的渐近估计

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基金项目: 韩国国家研究基金会资助项目(NRF2010-0012215)

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

Department of Applied Mathematics, Hanyang University, Ansan, Gyeonggido 426-791, Korea

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/)．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．
- 空间衰减界 /
- 微分不等式 /
- 衰减率
Abstract: 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 O(exp{-z²/[4(t+t₀)]}) for an L^2p cross-sectional measure of the solution 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.
- spatial decay bound /
- differential inequality /
- decay rate

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