Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media
Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media
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DOI：
10.1017/s0308210500002341
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发表时间：
2003-02
期刊：
影响因子：
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通讯作者：
K. Nishihara
中科院分区：
文献类型：
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作者：
K. Nishihara
考虑通过多孔介质的一维可压缩流的柯西问题，Hsiao和Liu证明了解（λ，u）表现为扩散波（λ，u λ），即由于达西定律的多孔介质方程的解。Nishihara及其同事已经得到了最优收敛速度。当λ 0（x）在x = ±∞处具有相同的常数状态时，所得到的收敛速度λ（λ − λ）（·，t）λ L∞ = O（t−1）是“最优的”，因为λ λ（·，t）λ L ∞ = O（t−1/2）。然而，这种“最佳”收敛速度不足以确定扩散波的位置。在本文中，我们的目标是通过选择适当的扩散波，以获得“真正最优”的收敛速度。
Consider the Cauchy problem for a one-dimensional compressible flow through porous media, Hsiao and Liu showed that the solution (υ, u) behaves as the diffusion wave (ῡ, ū), i.e. the solution of the porous-media equation due to the Darcy law. The optimal convergence rates have been obtained by Nishihara and co-workers. When υ0(x) has the same constant state at x = ±∞, the convergence rate ‖(υ − ῡ)(·,t)‖L∞ = O(t−1) obtained is ‘optimal’, since ‖ῡ(·,t)‖∞ = O(t−1/2). However, this ‘optimal’ convergence rate is less sufficient to determine the location of the diffusion wave. Our aim in this paper is to obtain the ‘truly optimal’ convergence rate by choosing suitably located diffusion waves.