Asymptotic behavior of solutions of the Hamer equation
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A. A. Solov′ev
Translated by: A. Plotkin - St. Petersburg Math. J. 26 (2015), 463-477
- DOI: https://doi.org/10.1090/S1061-0022-2015-01346-0
- Published electronically: March 20, 2015
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Abstract:
In a preceding paper the leading term was found for the asymptotics as $t\to +\infty$ of the solution of the initial problem for the Hamer equation, which is a simplest model for the motion of a radiating gas. Here, the second asymptotic term is constructed. It is proved that this term is proportional to the second term of the asymptotics of the solution of the initial problem for the Burgers equation.References
- Shuichi Kawashima and Yoshihito Tanaka, Stability of rarefaction waves for a model system of a radiating gas, Kyushu J. Math. 58 (2004), no. 2, 211–250. MR 2117245, DOI 10.2206/kyushujm.58.211
- K. Hamer, Nonlinear effects on the propagation of sound waves in a radiating gas, Quart. J. Mech. Appl. Math. 24 (1971), 155–168.
- K. Ito, BV-Solution of a hyperbolic-elliptic system for a radiating gas, Hokkaido Univ., Preprint, no. 368, 1997, 33 pp.
- Yongqin Liu and Shuichi Kawashima, Asymptotic behavior of solutions to a model system of a radiating gas, Commun. Pure Appl. Anal. 10 (2011), no. 1, 209–223. MR 2746535, DOI 10.3934/cpaa.2011.10.209
- Corrado Lattanzio and Pierangelo Marcati, Global well-posedness and relaxation limits of a model for radiating gas, J. Differential Equations 190 (2003), no. 2, 439–465. MR 1970037, DOI 10.1016/S0022-0396(02)00158-4
- Philippe Laurençot, Asymptotic self-similarity for a simplified model for radiating gases, Asymptot. Anal. 42 (2005), no. 3-4, 251–262. MR 2138795
- A. A. Solov′ev, The leading term of the asymptotics of the solution of the Hamer equation, Dokl. Akad. Nauk 439 (2011), no. 6, 740–742 (Russian); English transl., Dokl. Math. 84 (2011), no. 1, 555–557. MR 2883803, DOI 10.1134/S1064562411050127
- Denis Serre, $L^1$-stability of constants in a model for radiating gases, Commun. Math. Sci. 1 (2003), no. 1, 197–205. MR 1979850
Bibliographic Information
- A. A. Solov′ev
- Affiliation: Mathematics Department, Chelyabinsk State University, ul. Brat′ev Kashirinykh 129, Chelyabinsk 454001, Russia
- Email: alsol@csu.ru
- Received by editor(s): March 18, 2013
- Published electronically: March 20, 2015
- Additional Notes: Supported by RFBR (grant no. 12-01-00259-a)
- © Copyright 2015 American Mathematical Society
- Journal: St. Petersburg Math. J. 26 (2015), 463-477
- MSC (2010): Primary 35G55
- DOI: https://doi.org/10.1090/S1061-0022-2015-01346-0
- MathSciNet review: 3289180