We obtain the global existence of weak solutions for the Cauchy problem of the nonhomogeneous, resonant system. First, by using the technique given in Tsuge (2006), we obtain the uniformly bounded estimates and when is increasing (similarly, and when is decreasing) for the -viscosity and -flux approximation solutions of nonhomogeneous, resonant system without the restriction or as given in Klingenberg and Lu (1997), where and are Riemann invariants of nonhomogeneous, resonant system; is a uniformly bounded function of depending only on the function given in nonhomogeneous, resonant system, and is the bound of . Second, we use the compensated compactness theory, Murat (1978) and Tartar (1979), to prove the convergence of the approximation solutions.
"Global Existence of Solutions for a Nonstrictly Hyperbolic System." Abstr. Appl. Anal. 2014 (SI08) 1 - 7, 2014. https://doi.org/10.1155/2014/691429