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Non-local conservation laws

The initial-boundary value problem for general non-local scalar conservation laws in one space dimension

The initial-boundary value problem for general non-local scalar conservation laws in one space dimension

... on non-local conservation laws, proving existence and eventually unique- ness of solutions of the Cauchy problem for ...the non- local term, which may exceed the boundaries of ...

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Non-local conservation laws for traffic flow modeling

Non-local conservation laws for traffic flow modeling

... with non-local fluxes and adapted numerical schemes to compute approximate solutions to such kind of ...scalar conservation laws with non-local flux arising in traffic ...scalar ...

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Solutions of kinetic equations related to non-local conservation laws

Solutions of kinetic equations related to non-local conservation laws

... e-mail: Florent.BERTHELIN@univ-cotedazur.fr Abstract The aim of this paper is to propose kinetic models associated with conservation laws with a non-local flux and to prove the existence of ...

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Well-posedness of IBVP for 1D scalar non-local conservation laws

Well-posedness of IBVP for 1D scalar non-local conservation laws

... The local 1D IBVP We recall below some results concerning the classical (local) one dimensional initial boundary value problem for a scalar conservation ...

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High order numerical schemes for one-dimension non-local conservation laws

High order numerical schemes for one-dimension non-local conservation laws

... NON-LOCAL CONSERVATION LAWS CHRISTOPHE CHALONS A , PAOLA GOATIN B , AND LUIS ...of non-local conservation laws in one space ...

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Non Local Conservation Laws in Bounded Domains

Non Local Conservation Laws in Bounded Domains

... Model, Non-Local Conservation Laws. 1 Introduction Non local conservation laws are being developed to model various phenomena, such as the dynamics of crowd, see ...

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Crowd Dynamics through Non-Local Conservation Laws

Crowd Dynamics through Non-Local Conservation Laws

... through Non-Local Conservation Laws Aekta Aggarwal 1 Paola Goatin 1 Abstract We present a Lax–Friedrichs type scheme to compute the solutions of a class of non-local and ...

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Stability estimates for non-local scalar conservation laws

Stability estimates for non-local scalar conservation laws

... Scalar conservation laws; Non-local flux; ...Introduction Conservation laws with non-local flux have drawn growing attention in the recent ...

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Microscopic local conservation laws for classical fluids

Microscopic local conservation laws for classical fluids

... respectively. Integration by parts yields the local conservation law of momentum, owing to the stationarity of S for arbitrary a(r, t). In the above derivation of the momentum balance at the point r, after ...

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Modeling traffic on urban road networks with hyperbolic conservation laws

Modeling traffic on urban road networks with hyperbolic conservation laws

... Following the ideas introduced in [108] and observing that situations with unbounded acceleration only appear for specific initial datum, we derive a model in which accelerating vehicles are treated as moving ...

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A non-local scalar conservation law describing navigation processes

A non-local scalar conservation law describing navigation processes

... [19] M. Lécureux-Mercier. Improved stability estimates on general scalar bal- ance laws. J. Hyper. Diff. Eq., 8(4):727–757, 2011. [20] L. Gómez Nava, R. Grossmann, and F. Peruani. Markov robots: minimal navigation ...

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Optimal Regularizing Effect for Scalar Conservation Laws

Optimal Regularizing Effect for Scalar Conservation Laws

... (9) (∂t + a ′ (v)∂x)f = ∂ γ v m where a is a smooth function while m is a bounded, signed Radon measure on R + × R × R, and γ ∈ N. Transport equations of this type naturally appear in the kinetic formulation of ...

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On a Hamiltonian regularization of scalar conservation laws

On a Hamiltonian regularization of scalar conservation laws

... SCALAR CONSERVATION LAWS BILLEL GUELMAME ...scalar conservation law (SCL), which is obtained by modifying its ...of local smooth solutions are given in this ...

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Scalar conservation laws with rough (stochastic) fluxes

Scalar conservation laws with rough (stochastic) fluxes

... Throughout the paper we adopt the notation and terminology of stochastic calculus. In general du denotes some kind of time differential, while in the case of (3) is the usual stochastic differential. Similarly in the ...

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General constrained conservation laws. Application to pedestrian flow modeling.

General constrained conservation laws. Application to pedestrian flow modeling.

... on conservation laws with local flux constraint obtained in [1, 9] to general flux functions and nonclassical solutions arising for example in pedestrian flow ...

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On the maximal smoothing effect for multidimensional scalar conservation laws

On the maximal smoothing effect for multidimensional scalar conservation laws

... f is strictly convex in a right neighborhood of 0. To have f 0 (0) = 0 it is enough to make a change of space variable: x←→ x − f 0 (0)t . For the right local convexity it is assumed that f (1+d) (0) > 0 . In ...

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Euler-Lagrange change of variables in conservation laws

Euler-Lagrange change of variables in conservation laws

... for local existence of smooth solutions by an argument for first order symmetrizable hyperbolic systems, to Chae-Huh [12] for global existence with small initial data, and also to [11] for the solutions beyond ...

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Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws

Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws

... FOR UNCERTAIN SCALAR CONSERVATION LAWS J. TRYOEN † ‡ , O. LE MAˆITRE ‡ , AND A. ERN † Abstract. This paper deals with the design of adaptive anisotropic discretization schemes for conservation ...

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Applications of the DFLU flux to systems of conservation laws

Applications of the DFLU flux to systems of conservation laws

... Scalar conservation laws like equation (1) with a flux function discontinuous in space have been the object of many studies [7, 17, 14, 8, 10, 13, 24, 25, 6, 20, 2, ...one local maximum and the same ...

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Numerical Methods for the solution of Hyperbolic Conservation Laws

Numerical Methods for the solution of Hyperbolic Conservation Laws

... Godunov’s method is an example of conservative scheme. In this method, the solution is considered as piecewise constant over each mesh cell at a fixed time and the evolution of the solution to the next time step results ...

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