TY - JOUR
T1 - Convergence rates towards the traveling waves for a model system of radiating gas with discontinuities
AU - Ohnawa, Masashi
PY - 2012
Y1 - 2012
N2 - The present paper is concerned with the asymptotic behavior of a discontinuous solution to a model system of radiating gas. As we assume that an initial data has a discontinuity only at one point, so does the solution. Here the discontinuous solution is supposed to satisfy an entropy condition in the sense of Kruzkov. Previous researches have shown that the solution converges uniformly to a traveling wave if an initial perturbation is integrable and is small in the suitable Sobolev space. If its anti-derivative is also integrable, the convergence rate is known to be (1+t)-1/4 as time t tends to infnity. In the present paper, we improve the previous result and show that the convergence rate is exactly the same as the spatial decay rate of the initial perturbation.
AB - The present paper is concerned with the asymptotic behavior of a discontinuous solution to a model system of radiating gas. As we assume that an initial data has a discontinuity only at one point, so does the solution. Here the discontinuous solution is supposed to satisfy an entropy condition in the sense of Kruzkov. Previous researches have shown that the solution converges uniformly to a traveling wave if an initial perturbation is integrable and is small in the suitable Sobolev space. If its anti-derivative is also integrable, the convergence rate is known to be (1+t)-1/4 as time t tends to infnity. In the present paper, we improve the previous result and show that the convergence rate is exactly the same as the spatial decay rate of the initial perturbation.
KW - Asymptotic stability
KW - Convergence rate
KW - Hyperbolic-elliptic coupled system
KW - Shock wave
KW - Weighted energy method
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U2 - 10.3934/krm.2012.5.857
DO - 10.3934/krm.2012.5.857
M3 - Article
AN - SCOPUS:84872184419
VL - 5
SP - 857
EP - 872
JO - Kinetic and Related Models
JF - Kinetic and Related Models
SN - 1937-5093
IS - 4
ER -