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About some global solutions for quasilinear hyperbolic equations. Funkcialaj ekvacioj 11:51-57. Chang Tung and Hiao Ling (1977). Riemann problem and discontinuous initial value problem for a typical quasilinear hyperbolic system without convexity. Acta Math. Sinica 20:229-231 (in Chinese). Ying Lungan and Wang Chinghua (1980). Global solutions of the Cauchy problem for an inhomogeneous quasilinear hyperbolic system. Comm. PureAppl.
Math. 33:579-597. Hsiao Ling and Zhang Tong (1978). Riemann problem for 2 × 2 quasilinear hyperbolic systems without convexity. Kexue Tongbao 8:465–469 (in Chinese). We deal with non-linear conservation laws and strive to establish a realistic multidimensional framework. The main question that interests us is: “When can we use hyperbolic (simplified) models?” and to answer this, we study the limits of dispersion of zero diffusion. While our evidence establishes integrity, the focus is on reliability and error. In particular, we consider all known physically relevant solutions, both classic and non-classic. The techniques we use depend on an analytical attitude towards dimensional functional theory and are energy-based methods. Tartar L. (1979) Compensated compactness and applications to partial differential equations.
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Sinica 11:314–323; 324-337; 12:132-143 (in Chinese). Abstract: We study the limiting behavior of solutions of a class of conservation laws with endangered nonlinear scattering and dispersion terms. We prove the convergence towards the entropic solution of the first-order problem under a condition of relative size of the terms of diffusion and dispersion. This work is motivated by the pseudoviscosity approximation introduced by Neumann in the 50s. For nonlinear hyperbolic systems of conservation laws, the initial problem of limit values is studied. Two formulations of boundary conditions are proposed: a limit inequality of entropy is derived using the viscosity method, and a second formulation is based on the Riemann problem. These two formulations are equivalent for linear systems and nonlinear scalar equations. For nonlinear systems, the second formulation leads to well-posed problems. The local nonlinear structure is studied. The p-system and the isentropic Euler equations are detailed. Li Caizhong; Hsiao Ling; Yang Shaoqi and Yuan Zuwen (1963), Riemann problem for a typical quasilinear hyperbolic system without convexity. Lax P.
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