Hyperbolic systems of conservation laws : the one-dimensional Cauchy problem

By Alberto Bressan. 2000

990 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c2f5eaad7406e570b41b9cd61d71aadab20ef9d7

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Citations in the corpus

Vanishing Viscosity Solutions of Nonlinear Hyperbolic Systems (2001, methodology): “For comprehensive account of the recent uniqueness and stability theory we refer to [ B5 ].”
Traffic Flow on a Road Network Using the Aw–Rascle Model (2006, methodology): “For the definition of an entropic solution, we refer to Bressan (2000).”
Source-Destination Flow on a Road Network (2005, methodology): “Classical theory of conservation laws, see [6], ensures, for every initial data in L(1), the existence of a weak entropic solution to (2.”
A traffic model for velocity data assimilation (2010, background): “Since transport equations such as (1) involve discontinuities which can appear in finite time even from smooth initial conditions (see [3]), weak entropy solutions to the density evolution model must be considered.”
A robust optimization approach for dynamic traffic signal control with emission considerations (2012, methodology): “1) can be found in Bressan (2000). For a detailed discussion of numerical schemes for conservation laws, we refer the reader to Godunov (1959) and LeVeque (1992). A well-known discrete version of the LWR model, the cell transmission model (CTM), was introduced by Daganzo (1994) and Daganzo (1995); t”
Interactions of delta shock waves for the transport equations with split delta functions (2009, unknown): “This is equivalent to say that we deal with the vacuum states like as the rarefaction waves and then approximate them by a large number of small amplitude non-physical shock waves proposed by Bressan [2].”
An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation (2005, unknown): “ipschitz continuity of the ﬂow, we can use the error estimate J u˜(t),µ˜t , u(t),µt ≤ eC 2t Zt 0 liminf h→0 1 h ·J ˜u(τ+h),µ˜τ+h , Φh u˜(τ),µ˜τ dτ (7.5) For a proof of (7.5), see pp. 25–27 in [B]. The conditions stated in Theorem 1 now imply that, at almost every time τ, the measure ˜µtis absolu”
An ill posed Cauchy problem for a hyperbolic system in two space dimensions (2003, background): “The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2].”
On the continuum approximation of the on-and-off signal control on dynamic traffic networks (2013, methodology): “A similar technique has been applied in Bressan and Han (2011), and the reader is referred to Friesz et al.”
Traffic Flow on a Road Network (2002, unknown): “Still it is possible to consider”