conservation laws
Event-based control of linear hyperbolic systems of conservation laws
... In this paper, event-based boundary controls to stabi- lize a linear hyperbolic system of conservation laws have been designed. The analysis of global exponential stabil- ity is based on Lyapunov ...
16
Robust feedforward boundary control of hyperbolic conservation laws
... hyperbolic conservation laws Xavier Litrico, Vincent Fromion and Gérard Scorletti Abstract— The paper proposes a feedforward boundary con- trol to reject measured disturbances for systems modelled by ...
7
Semigroup approach to conservation laws with discontinuous flux
... (for conservation laws in Ω l and Ω r ) we readily see that the solution is uniquely defined by the datum outside the triangle T := {(t, x) | t ∈ (0, T ], |x| ≤ Lt} where L = L 0 + ...
15
Applications of the DFLU flux to systems of conservation laws
... 1 Introduction The main difficulty in the numerical solution of systems of conservation laws is the complexity of con- structing the Riemann solvers. One way to overcome this difficulty is to consider ...
24
Fractional spaces and conservation laws
... and conservation laws Pierre CASTELLI, Pierre-Emmanuel JABIN, St´ephane JUNCA Abstract In 1994, Lions, Perthame and Tadmor conjectured the maximal smoothing effect for multidimensional scalar ...
10
Stability estimates for non-local scalar conservation laws
... scalar conservation laws Felisia Angela Chiarello 1 Paola Goatin 1 Elena Rossi 1 Abstract We prove the stability of entropy weak solutions of a class of scalar conservation laws with non-local ...
23
Conservation Laws with Unilateral Constraints in Traffic Modeling
... to the Riemann Problem (2.4) computed at time, say, t = 1. As it is usual when dealing with nonclassical scalar conservation laws, see [ 21 , Chapter II], we need first to introduce the auxiliary function ...
13
Viscoelastic flows of Maxwell fluids with conservation laws
... of conservation laws to model viscoelastic flows with Upper-Convected Maxwell fluids, either 3D compressible or 2D incompressible with hydrostatic pressure and a free ...
31
Non-local conservation laws for traffic flow modeling
... non-local conservation laws in one space dimension, given by a non-local multi-class model obtained as a generalization of the M -populations model for traffic flow described in [ 8 ...scalar ...
145
Monotonization of flux, entropy and numerical schemes for conservation laws
... 18 Adimurthi & G. D. Veerappa Gowda & J. Jaffr´e family includes the Force and proposes an alternative for the Musta schemes. For all these schemes we proved convergence of the approximate solution to the ...
22
Conservation laws in the modelling of collective phenomena
... Over the last decades, traffic congestion, car accidents and pollution became daily issues. To understand and overcome road traffic problems, scientists from different research fields are creating advanced mathematical ...
182
Optimal Regularizing Effect for Scalar Conservation Laws
... Since C. DeLellis and M. Westdickenberg [Ann. Inst. H. Poincar´ e Anal. Non Lin´ eaire 20 (2003), 1075–1085] have proved the existence of such solutions that do not belong to B q,loc s,p if either s > 1/ max(p, 3) or ...
25
General constrained conservation laws. Application to pedestrian flow modeling.
... Besides, Colombo and Rosini [12] introduced a model for pedestrian flow accounting for panic appearance and consisting in a scalar conservation law in one space-dimension displaying nonclassical shocks. Such a ...
36
On the maximal smoothing effect for multidimensional scalar conservation laws
... [3] P. Castelli, S. Junca. Smoothing eect in BV − Φ for scalar conservation laws. preprint (2015), hal-01133725, 28 pp. [4] G.-Q. Chen, S. Junca, M. Rascle. Validity of nonlinear geometric optics for ...
15
Nonlocal systems of conservation laws in several space dimensions
... ∂ t U 2 + ∂ x U 2 ϕ(U ) = 0 (3.6) is a 2 × 2 system of conservation laws in one space dimension in the unknown U = (U 1 , U 2 ). System (3.6) has been extended and studied from many different points of ...
23
Modeling traffic on urban road networks with hyperbolic conservation laws
... Solving conservation laws on networks is not trivial, because of the difficulty of modeling the dynamics at the junctions, and more precisely the fact that the boundary conditions on incoming and outgoing ...
150
Numerical Methods for the solution of Hyperbolic Conservation Laws
... Hyperbolic Conservation Laws ...hyperbolic conservation laws in the one-dimensional scalar case, by studying Godunov and van Leer’s ...hyperbolic conservation laws, a theoretical ...
30
L1 and L8 intermediate asymptotics for scalar conservation laws
... [13] T.-P. Liu & T. Yang, A new entropy functional for a scalar conservation law, Commun. Pure Appl. Math. 52 no. 11 (1999), 1427–1442. [14] D. Serre, Systems of conservation laws – 1. ...
20
Euler-Lagrange change of variables in conservation laws
... pairs of the ABI equations. An explicit formula of the entropy solution of the BI equations is also given. Finally, we remark that the equivalence of the two coordinate systems in several space dimensions is discussed ...
29
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 ...
23