Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media

Kenji Nishihara

研究成果: Article

18 引用 (Scopus)

抄録

Consider the Cauchy problem for a one-dimensional compressible flow through porous media, vt - ux = 0, x ∈ R, t > 0, ut + p(v)x = -αu, (v, u)|t=0 = (v0, u0) (x). Hsiao and Liu showed that the solution (v, u) behaves as the diffusion wave (v̄, ū), i.e. the solution of the porous-media equation due to the Daroy law. The optimal convergence rates have been obtained by Nishihara and co-workers. When v0(x) has the same constant state at x = ±∞, the convergence rate ∥(v - v̄)(·, t)∥L∞ = O(t-1 obtained is 'optimal', since ∥v̄(·, 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.

元の言語 English 177-196 20 Royal Society of Edinburgh - Proceedings A 133 1 Published - 2003

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Optimal Convergence Rate
Compressible flow
Compressible Flow
Porous Media
Porous materials
Porous Medium Equation
Convergence Rate
Cauchy Problem
Sufficient

ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

これを引用

：: Royal Society of Edinburgh - Proceedings A, 巻 133, 番号 1, 2003, p. 177-196.

研究成果: Article

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