TalksA version of the Glimm method based on generalized Riemann problems.
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We introduce a generalization of Glimm's random choice method which provides an approximation of the entropy solution to the Cauchy problem associated with a quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend on the unknown as well as on the time and space variables. The method is based on local approximate solutions of the generalized Riemann problem, which form building block in our scheme. We study the nonlinear interactions between generalized wave patterns and establish the stability of the approximations. This analysis leads us to a global existence result for quasilinear hyperbolic systems with source-term. Our result applies, for instance, to the compressible Euler equations in general geometries and to hyperbolic systems posed on a Lorentzian manifold.
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Meng-Kai Hong
2008-01-16
15:10:00 - 16:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
We introduce a generalization of Glimm's random choice method which provides an approximation of the entropy solution to the Cauchy problem associated with a quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend on the unknown as well as on the time and space variables. The method is based on local approximate solutions of the generalized Riemann problem, which form building block in our scheme. We study the nonlinear interactions between generalized wave patterns and establish the stability of the approximations. This analysis leads us to a global existence result for quasilinear hyperbolic systems with source-term. Our result applies, for instance, to the compressible Euler equations in general geometries and to hyperbolic systems posed on a Lorentzian manifold.