Initial Boundary Value Problem for the System of Compressible Adiabatic Flow Through Porous Media
Initial Boundary Value Problem for the System of Compressible Adiabatic Flow Through Porous Media
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DOI：
10.1006/jdeq.1999.3648
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发表时间：
1999-11
影响因子：
2.4
通讯作者：
L. Hsiao;R. Pan
中科院分区：
文献类型：
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作者：
L. Hsiao;R. Pan
本文研究了一维可压缩绝热渗流方程组在固定边界条件下的初值问题。在初始值振荡的约束下，通过特征分析和能量估计相结合的方法，证明了经典解的整体存在性和大时间性态.找到了解的时间渐近状态，并证明了解的指数收敛性。它还表明，这个问题可以很好的时间渐近近似的初始边界问题的相关扩散方程从原来的双曲型系统的达西定律，提供的初始总质量是相同的。这两个解决方案之间的差异趋于零指数快，因为时间去到无穷大的意义上的H 1。由此观察到边界效应阻尼机制引起的扩散现象。
Abstract We study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition. Under the restriction on the oscillations in the initial data, we establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and energy estimate methods. The time-asymptotic states for the solution are found and the exponential convergence to the asymptotic states is proved. It is also shown that this problem can be approximated very well time-asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by Darcy's law, provided that the initial total mass is the same. The difference between these two solutions tends to zero exponentially fast as time goes to infinity in the sense of H 1 . The diffusive phenomena caused by damping mechanism with boundary effects are thus observed.