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Article
Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes
Hyperbolic conservation laws arise in the context of continuum physics, and are mathematically presented in differential form and understood in the distributional (weak) sense. The formal application of the Ga...
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Article
Preface to the Focused Issue in Honor of Professor Tong Zhang on the Occasion of His 90th Birthday
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Article
Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws
This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the “meaningful objects” are the fluxes, e...
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Article
Transversal effects of high order numerical schemes for compressible fluid flows
Finite volume schemes for the two-dimensional (2D) wave system are taken to demonstrate the role of the genuine dimensionality of Lax-Wendroff flow solvers for compressible fluid flows. When the finite volume ...
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Article
Entropy convergence of new two-value scheme with slope relaxation for conservation laws
This paper establishes the entropy convergence of a new two-value high resolution finite volume scheme with slope relaxation for conservation laws. This scheme, motivated by the general method of high resoluti...
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Article
Explicit construction of measure solutions of Cauchy problem for transportation equations
The transportation equations are a mathematical model of zero-pressure flow in gas dynamics and the adhesion particle dynamics system to explain the formation of large scale structures in the universe. With th...