Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-18T07:48:21.423Z Has data issue: false hasContentIssue false
  • English
  • Français

Cauchy problem for an extended model of combustion

Published online by Cambridge University Press:  14 November 2011

Yun-guang Lu
Yun-guang Lu
Affiliation:
Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Synopsis

This paper considers the Cauchy problem for an extended model of combustion (u + qz)t + f(u)x = 0, zt + kg(u)z = 0 with Lp bounded initial data, where g(u) is a piecewise Lipschitz continuous function and its discontinuous points have no finite limit point. The integral representation gives a definition of a weak solution in Lp space. Some existence results are obtained based on a simplified method of compensated compactness in which the weak continuity theorem of 2 * 2 determinants plays a more important role, but the idea of Young measures has been avoided.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 3-4 , 1992 , pp. 349 - 360
Copyright
Copyright © Royal Society of Edinburgh 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Majda, A.. A qualitative model for dynamic combustion. SIAM J. Appl. Math. 41 (1981), 70–93.CrossRefGoogle Scholar
2Lung-an, Ying and Zhen-huan, Teng. A hyperbolic model of combustion. Lecture Notes Numer. Appl. Anal. 5 (1982), 409–434.Google Scholar
3Lung-an, Ying and Zhen-huan, Teng. Riemann problem for a reacting and convection hyperbolic system. Approx. Theory Appl. 1 (1984), 95–122.Google Scholar
4Zhen-huan, Teng and Lung-an, Ying. A model of combustion for infinite rate of reaction. Annual Math. 7A(3) (1986), 315–324.Google Scholar
5Dafermos, C. M.. Characteristics in hyperbolic conservation laws, a study of the structure and the asymptotic behavior of solutions. In Nonlinear Analysis and Mechanics Vol. 1 (London: Pitman, 1977).Google Scholar
6Lu, Yunguang. Cauchy Problem for a hyperbolic model (to appear).Google Scholar
7Schonbek, M. E.. Convergence of solutions to nonlinear dispersive equations. Comm. Partial Differential Equations 8 (1982), 959–1000.Google Scholar
8Lu, Yunguang. Convergence of solutions to nonlinear dispersive equations without convexity conditions. Appl. Anal. 31 (1989), 239–246.Google Scholar
9Tartar, T.. Compensated compactness and applications to partial differential equations. In Research notes in mathematics, nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. 4 ed. R. J. Knops, (New York: Pitman Press, 1979).Google Scholar