Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves

By Philippe G. LeFloch, J. Novotný. 2002

405 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/643d4994cd60ebf7c3ee25e263453d803663c239

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Citations in the corpus

Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems (2003, background): “• Nonclassical shocks and a host of nonlinear phenomena are governed by a borderline balance between dissipative and dispersive forces: we refer, for example, to the recent phase transitions studies of LeFloch and co-workers (LeFloch 2002).”
OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS (2005, neutral): “This is analogous to the situation with non-classical solutions for conservation laws (see LeFloch [ 26 ] and references therein for a detailed account of non-classical solutions for conservation laws).”
A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation (2006, background): “We refer to the book of LeFloch ( 2002 ) for an introduction to the highly active field of nonclassical shocks in (systems of) conservation laws.”
Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces (2014, background): “Weak solutions in general may not be unique [24,35].”
Pedestrian flows and non‐classical shocks (2005, background): “As a general reference for the theory of nonclassical solutions to conservation laws, see [18] [19].”
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains (2013, background): “and because an entropy dissipative regularization [12] requires that w x f (v) ≥ 0, ∀w.”
Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system (2010, methodology): “For the well-posedness problems, we refer to the works [5, 6, 24, 29] (and the references therein) in the content of weak solutions to systems (including scalar case) in conservation laws, and [26, 28] in the content of classical solutions to general quasi-linear hyperbolic systems.”
Dynamic capillary effects in heterogeneous porous media (2007, background): “Moreover, for some parameter settings, one can show that traveling wave solutions do not exist, and we have to consider different types of solution profiles (see, e.g., [ 13 ]).”