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Discretization of Unsteady Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis, 2002Summary: A basic target algorithm for approximating unsteady hyperbolic conservation laws uses a finite volume formulation in three steps: recovery or reconstruction of a more accurate approximation from a set of cell averages; solution of the conservation law to obtain interface fluxes averaged over a time step; and computation of new cell averages at
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On Hyperbolic Systems of Conservation Laws
Differential Equations, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Well-posedness theory for hyperbolic conservation laws
Communications on Pure and Applied Mathematics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Tai-Ping, Yang, Tong
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Hyperbolic Conservation Laws and L2
2018Taking as background the fact that conservation laws in a single space variable are well-posed in the space of functions of bounded variation, while multidimensional systems enjoy short-time well-posedness in Sobolev spaces Hs, we attempt to resolve the discrepancies between these two theories by exploring what can be said about stability of one ...
Barbara Lee Keyfitz, Hao Ying
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Divergence-Measure Fields and Hyperbolic Conservation Laws
Archive for Rational Mechanics and Analysis, 1999The authors study a class of vector fields \(F\in L^\infty(D,{\mathbb R}^N)\), \(D\subset{\mathbb R}^N\), such that \(\operatorname {div}F\) coincides some finite Borel measure in the sense of distributions. Such vector fields, called divergence-measure fields, are proved to take normal traces over subsets with Lipschitz boundaries and to satisfy ...
Chen, Gui-Qiang, Frid, Hermano
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HIGH RESOLUTION SCHEMES FOR HYPERBOLIC CONSERVATION LAWS
1993The basic theory of second-order total variance diminishing schemes for scalar conservation laws is discussed. Then an approach of extending this technique to systems of equations is proposed. A class of limiters is presented which includes a discontinuous limiter due to the author. Various limiters are compared numerically.
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Hyperbolic Systems of Conservation Laws
1983The study of systems of quasilinear hyperbolic equations that result from the balance laws of continuum physics was initiated more than a century ago yet, despite considerable progress in recent years, most of the fundamental problems in the analytical theory remain unsolved.
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Upwind bicompact schemes for hyperbolic conservation laws
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâFor the first time, upwind bicompact schemes of third order approximation in space are presented. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with integration in time by a Runge–Kutta method. Stability and monotonicity of the first-order in time scheme are investigated, dissipative and dispersion ...
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