Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media

Kenji Nishihara; Masataka Nishikawa

doi:10.1137/S003614109936467X

Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media

Kenji Nishihara^*, Masataka Nishikawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Hsiao and Serre in [Chinese Ann. Math. Ser. B, 16B (1995), pp. 1-14] showed the solution to the system {v_t - u_x = 0, (t,x) ∈ R₊ × R, u_t + p(v,s)_x = -αu, α > 0, st = 0 with initial data (v,u,s)(0,x) = (v_o, u_o, s_o) (x) → (v, u_±, s) as x → ±∞ tends to the following nonlinear parabolic equation time-asymptotically: {v̄_t = -1/αp(v̄,s_o)_xx, (t,x) ∈ R₊ × R, ū = 1/αp(v̄,s_o)_x. In this paper we find its convergence rate, which will be optimal.

Original language	English
Pages (from-to)	216-239
Number of pages	24
Journal	SIAM Journal on Mathematical Analysis
Volume	33
Issue number	1
DOIs	https://doi.org/10.1137/S003614109936467X
Publication status	Published - 2001

Keywords

Asymptotic behavior
Convergence rate
The system of compressible adiabatic flow

ASJC Scopus subject areas

Mathematics(all)
Analysis
Applied Mathematics

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10.1137/S003614109936467X

Cite this

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title = "Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media",

abstract = "Hsiao and Serre in [Chinese Ann. Math. Ser. B, 16B (1995), pp. 1-14] showed the solution to the system {vt - ux = 0, (t,x) ∈ R+ × R, ut + p(v,s)x = -αu, α > 0, st = 0 with initial data (v,u,s)(0,x) = (vo, uo, so) (x) → (v, u±, s) as x → ±∞ tends to the following nonlinear parabolic equation time-asymptotically: {{\=v}t = -1/αp({\=v},so)xx, (t,x) ∈ R+ × R, ū = 1/αp({\=v},so)x. In this paper we find its convergence rate, which will be optimal.",

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author = "Kenji Nishihara and Masataka Nishikawa",

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T1 - Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media

AU - Nishihara, Kenji

AU - Nishikawa, Masataka

PY - 2001

Y1 - 2001

N2 - Hsiao and Serre in [Chinese Ann. Math. Ser. B, 16B (1995), pp. 1-14] showed the solution to the system {vt - ux = 0, (t,x) ∈ R+ × R, ut + p(v,s)x = -αu, α > 0, st = 0 with initial data (v,u,s)(0,x) = (vo, uo, so) (x) → (v, u±, s) as x → ±∞ tends to the following nonlinear parabolic equation time-asymptotically: {v̄t = -1/αp(v̄,so)xx, (t,x) ∈ R+ × R, ū = 1/αp(v̄,so)x. In this paper we find its convergence rate, which will be optimal.

AB - Hsiao and Serre in [Chinese Ann. Math. Ser. B, 16B (1995), pp. 1-14] showed the solution to the system {vt - ux = 0, (t,x) ∈ R+ × R, ut + p(v,s)x = -αu, α > 0, st = 0 with initial data (v,u,s)(0,x) = (vo, uo, so) (x) → (v, u±, s) as x → ±∞ tends to the following nonlinear parabolic equation time-asymptotically: {v̄t = -1/αp(v̄,so)xx, (t,x) ∈ R+ × R, ū = 1/αp(v̄,so)x. In this paper we find its convergence rate, which will be optimal.

KW - Asymptotic behavior

KW - Convergence rate

KW - The system of compressible adiabatic flow

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Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media

Abstract

Keywords

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