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Lu, Yun-Guang 2002. Singular Limits of Stiff Relaxation and Dominant Diffusion for Nonlinear Systems. Journal of Differential Equations, Vol. 179, Issue. 2, p. 687.
Yang, Tong Zhu, Changjiang and Zhao, Huijiang 1998. Compactness Framework ofLpApproximate Solutions for Scalar Conservation Laws. Journal of Mathematical Analysis and Applications, Vol. 220, Issue. 1, p. 164.
Kurganov, A. and Tadmor, E. 1997. Stiff Systems of Hyperbolic Conservation Laws: Convergence and Error Estimates. SIAM Journal on Mathematical Analysis, Vol. 28, Issue. 6, p. 1446.
Klingenberg, Christian and Lu, Yun-guang 1996. Cauchy problem for hyperbolic conservation laws with a relaxation term. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 126, Issue. 04, p. 821.
Lu, Yunguang 1994. Convergence of the viscosity method for some nonlinear hyperbolic systems. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 124, Issue. 02, p. 341.
Lu, Yunguang 1994. Cauchy problem for a hyperbolic model. Nonlinear Analysis: Theory, Methods & Applications, Vol. 23, Issue. 9, p. 1135.
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.
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