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It is proved that for scalar conservation laws, if the flux function is strictly convex, and if the entropy solution is piecewise smooth with finitely many discontinuities (which includes initial central rarefaction waves, initial shocks, possible spontaneous formation of shocks in a future time and interactions of all these patterns), then the error of… (More)

- Haitao Fan, Shi Jin, Zhen-Huan Teng, Typeset By, A M S-T
- 1998

In this paper we study the zero reaction limit of the hyperbolic conservation law with stii source term @ t u + @ x f(u) = 1 u(1 ? u 2) : For the Cauchy problem to the above equation, we prove that as ! 0, its solution converges to piecewise constant (1) solution, where the two constants are the two stable local equilibrium. The constants are separated by… (More)

In this paper we address the questions of the convergence rate for approximate solutions to conservation laws with piecewise smooth solutions in a weighted W 1,1 space. Convergence rate for the derivative of the approximate solutions is established under the assumption that a weak pointwise-error estimate is given. In other words, we are able to convert… (More)

- Yan-Xiang Kan, Tao Tang, Zhen-Huan Teng
- 2001

We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise… (More)

The initial value problem of convex conservation laws, which includes the famous Burgers' (inviscid) equation, plays an important rule not only in theoretical analysis for conservation laws, but also in numerical computations for various numerical methods. For example, the initial value problem of the Burgers' equation is one of the most popular benchmarks… (More)

We analyze the convergence for relaxation approximation applied to conservation laws with stii source terms. We suppose that the source term q(u) is dissipative. Semi-implicit relaxing schemes are investigated and the corresponding stability theory is established. In particular, we proved that the numerical solution of a rst-order relaxing scheme is… (More)

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