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 IJMNTA  Vol.2 No.3 , September 2013
Pointwise Estimates for Solutions to a System of Radiating Gas
Abstract:

In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtain the pointwise decay estimates of solutions to the problem.

Cite this paper: S. Mao and Y. Liu, "Pointwise Estimates for Solutions to a System of Radiating Gas," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 3, 2013, pp. 186-193. doi: 10.4236/ijmnta.2013.23026.
References

[1]   R. Courant and K. O. Friedrichs, “Supersonic Flow and ShockWaves,” Interscience Publishers, Inc., New York, 1948.

[2]   W. G. Vincenti and C. H. Kruger, “Introduction to Physical Gas Dynamics,” Wiley, New York, 1965.

[3]   K. Hamer, “Nonlinear Effects on the Propogation of Sound Waves in a Radiating Gas,” Quarterly Journal of Mechanics & Applied Mathematics, Vol. 24, No. 2, 1971, pp. 155-168. http://dx.doi.org/10.1093/qjmam/24.2.155

[4]   W. L. Gao and C. J. Zhu, “Asymptotic Decay toward the Planar Rarefaction Waves for a Model System of the Radiating Gas in Two Dimensions,” Mathematical Models and Methods in Applied Sciences, Vol. 18, No. 4, 2008, pp. 511-541. http://dx.doi.org/10.1142/S0218202508002760

[5]   S. Kawashima and S. Nishibata, “Weak Solutions with a Shock to a Model System of the Radiating Gas,” Science Bulletin of Josai University, Vol. 5, Special Issue, 1998, pp. 119-130.

[6]   S. Kawashima and S. Nishibata, “Cauchy Problem for a Model System of the Radiating Gas: Weak Solution with a Jump and Classical Solutions,” Mathematical Models and Methods in Applied Sciences, Vol. 9, No. 1, 1999, pp. 69-91. http://dx.doi.org/10.1142/S0218202599000063

[7]   M. D. Francesco, “Initial Value Problem and Relaxation Limits of the Hamer Model for Radiating Gases in Several Space Variables,” Nonlinear Differential Equations and Applications NoDEA, Vol. 13, No. 5-6, 2007, pp. 531-562. http://dx.doi.org/10.1007/s00030-006-4023-y

[8]   Y. Liu and S. Kawashima, “Asymptotic Behavior of Solutions to a Model System of a Radiating Gas,” Communications on Pure and Applied Analysis, Vol. 10, No. 1, 2011, pp. 209-223. http://dx.doi.org/10.3934/cpaa.2011.10.209

[9]   W.-K. Wang and T. Yang, “The Pointwise Estimates of Solutions for Euler Equations with Damping in Multi-Dimensions,” Journal of Differential Equations, Vol. 173, No. 2, 2001, pp. 410-450. http://dx.doi.org/10.1006/jdeq.2000.3937

 
 
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