Viscous shock wave tracing, local conservation laws, and pointwise estimates
Vol. 4 No. 3 (2009) P.235~P.297
We introduce a new approach to decompose a system of viscous conservation laws with respect to each characteristic wave
structures. Under this new decomposition, the global wave interactions of the system are reduced to coupling of nonlinear waves
around constant states outside shock region and a scalar conservation law in the shock region to determine the behavior of local
internal shock layers. The behavior is characterized by the motion of the viscous shock fronts. It is analyzed by the local conservation laws. We also introduce generalized diffusion waves to localize
waves in initial data.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
We prove stability of a viscous shock layer of 2x2 system; and obtain the optimal rate of convergence.
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