TY - JOUR
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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U2 - 10.1137/S003614109936467X
DO - 10.1137/S003614109936467X
M3 - Article
AN - SCOPUS:0035527622
VL - 33
SP - 216
EP - 239
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 1
ER -