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

UR - http://www.scopus.com/inward/record.url?scp=84872184419&partnerID=8YFLogxK

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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 -