| Summary: | 博士 === 國立中央大學 === 數學系 === 101 === We study the Cauchy problem for general nonlinear hyperbolic balance laws assuming time-oscillating fluxes and sources. Such nonlinear balance laws arise in, for instance, the nozzle flows of gas dynamics with time periodic ducts, traffic models incorporating lane changing effects model and shallow water equations with time-dependent river’s bottom. The global existence of weak solutions is established by a new version of the generalized Glimm method which incorporates asymptotic expansions of the fluxes and sources. We prove existence of weak solutions and demonstrate that they are indeed entropy solutions satisfying the entropy inequality. The approximate solutions of the perturbed Riemann problem, the building blocks of the generalized Glimm scheme, are constructed by a modified Lax method, and a generalized version of the wave interaction estimates are provided for the proof of stability. The consistency of the scheme is established by proving the weak convergence of the residuals and source terms, thereby extending the methods introduced in [12].
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