Kinetic formulation of conservation laws

By Benoit Perthame. 2002

301 citations recorded by the source corpus.

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Citations in the corpus

Velocity averaging, kinetic formulations, and regularizing effects in quasi‐linear PDEs (2007, methodology): “We mention the early works of [GLPS88], [DLM91] and their applications, in the context of nonlinear conservation laws, in [LPT94a, LPT94b, LPS96, JP02]; a detailed list of references can be found in [Pe02] and is revisited in Section 2 below.”
Degenerate parabolic stochastic partial differential equations (2013, background): “[20,23,24,26], or [27] for a general presentation) and stochastic setting (see [9]), and also in the case of deterministic degenerate parabolic equations of second-order (see [5]).”
Adjoint and Compensated Compactness Methods for Hamilton–Jacobi PDE (2010, methodology): “Scalar conservation laws Our kinetic formulation for Hamilton–Jacobi PDE is inspired by the corresponding approach to conservation laws due to Lions, Perthame and Tadmor [17,18] (see also Perthame [19]), but our methods, when applied to the latter, differ.”
Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients (2006, methodology): “By the method of compensated compactness, one can show a regularizing effect of conservation laws, since it yields a result of strong convergence of the solution with an hypothesis of weak convergence of the data (see also the application of kinetic formulation of conservation laws by Perthane, 200”
Mathematical tools for kinetic equations (2004, background): “We refer to [102] for further references on this huge subject.”
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation* (2009, methodology): “Indeed, for vertically averaged models such as the Saint-Venant system [7], efficient and robust numerical techniques (relaxation schemes [10], kinetic schemes [24], .”
Degenerate parabolic stochastic partial differential equations: Quasilinear case (2013, background): “Other references for kinetic or entropy solutions in the case of deterministic hyperbolic conservation laws include for instance [3], [14], [18], [24], [25].”
Scalar conservation laws with stochastic forcing (2010, background): “and then derives (7). See [ Per02 ] for precise references.”
Scalar conservation laws with rough (stochastic) fluxes (2013, methodology): “It is by now well established that the simplest way to handle conservation laws is through their kinetic formulation developed through a series of papers – see Perthame and Tadmor [27], Lions, Perthame and Tadmor [15], Perthame [24, 25], and Lions, Perthame and Souganidis [12].”
Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme (2003, unknown): “(a) Bed topography in the Cartesian coordinates ( ~ x ; ~ z ) and initial volume of the granular mass in the topography-linked coordinates ( x , z ) and (b) slope angle q ( x ) of the bed in degrees in the topography-linked coordinates ( x , z ). u ð x ; t ¼ 0 Þ ¼ 0 ; ð 60 Þ with K = 1.26 (cid:24) 1”