January  1997, 3(1): 35-58. doi: 10.3934/dcds.1997.3.35

Shift-differentiabilitiy of the flow generated by a conservation law

1. 

S.I.S.S.A., Via Beirut, 2-4, 34014 Trieste

2. 

Dipartimento di Scienze dell'Ambeinte e del Territorio, Via L. Emanueli, 15 Bicocca, 20126 Milano, Italy

Received  July 1996 Published  October 1996

The paper introduces a notion of "shift-differentials" for maps with values in the space BV. These differentials describe first order variations of a given function $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition.
Citation: Alberto Bressan, Graziano Guerra. Shift-differentiabilitiy of the flow generated by a conservation law. Discrete & Continuous Dynamical Systems - A, 1997, 3 (1) : 35-58. doi: 10.3934/dcds.1997.3.35
[1]

Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 329-350. doi: 10.3934/dcds.2000.6.329

[2]

Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255

[3]

Afaf Bouharguane. On the instability of a nonlocal conservation law. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 419-426. doi: 10.3934/dcdss.2012.5.419

[4]

Robert I. McLachlan, G. R. W. Quispel. Discrete gradient methods have an energy conservation law. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1099-1104. doi: 10.3934/dcds.2014.34.1099

[5]

Julien Jimenez. Scalar conservation law with discontinuous flux in a bounded domain. Conference Publications, 2007, 2007 (Special) : 520-530. doi: 10.3934/proc.2007.2007.520

[6]

Raimund Bürger, Stefan Diehl, María Carmen Martí. A conservation law with multiply discontinuous flux modelling a flotation column. Networks & Heterogeneous Media, 2018, 13 (2) : 339-371. doi: 10.3934/nhm.2018015

[7]

Darko Mitrovic. Existence and stability of a multidimensional scalar conservation law with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (1) : 163-188. doi: 10.3934/nhm.2010.5.163

[8]

Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1337-1359. doi: 10.3934/dcdsb.2010.14.1337

[9]

Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Convergence of a finite volume scheme for a stochastic conservation law involving a $Q$-brownian motion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1459-1502. doi: 10.3934/dcdsb.2018159

[10]

Giuseppe Maria Coclite, Lorenzo Di Ruvo. A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1247-1282. doi: 10.3934/dcds.2017052

[11]

. Adimurthi, Siddhartha Mishra, G.D. Veerappa Gowda. Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes. Networks & Heterogeneous Media, 2007, 2 (1) : 127-157. doi: 10.3934/nhm.2007.2.127

[12]

Giuseppe Maria Coclite, Lorenzo di Ruvo. A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 2981-2990. doi: 10.3934/dcds.2016.36.2981

[13]

Christophe Chalons, Paola Goatin, Nicolas Seguin. General constrained conservation laws. Application to pedestrian flow modeling. Networks & Heterogeneous Media, 2013, 8 (2) : 433-463. doi: 10.3934/nhm.2013.8.433

[14]

Martin Gugat, Alexander Keimer, Günter Leugering, Zhiqiang Wang. Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Networks & Heterogeneous Media, 2015, 10 (4) : 749-785. doi: 10.3934/nhm.2015.10.749

[15]

Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Networks & Heterogeneous Media, 2019, 14 (4) : 709-732. doi: 10.3934/nhm.2019028

[16]

Anna Marciniak-Czochra, Andro Mikelić. A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 1065-1077. doi: 10.3934/dcdss.2014.7.1065

[17]

Jiří Neustupa. On $L^2$-Boundedness of a $C_0$-Semigroup generated by the perturbed oseen-type operator arising from flow around a rotating body. Conference Publications, 2007, 2007 (Special) : 758-767. doi: 10.3934/proc.2007.2007.758

[18]

Asim Aziz, Wasim Jamshed. Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 617-630. doi: 10.3934/dcdss.2018036

[19]

Van Cyr, John Franks, Bryna Kra, Samuel Petite. Distortion and the automorphism group of a shift. Journal of Modern Dynamics, 2018, 13: 147-161. doi: 10.3934/jmd.2018015

[20]

Daniel Gonçalves, Marcelo Sobottka. Continuous shift commuting maps between ultragraph shift spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1033-1048. doi: 10.3934/dcds.2019043

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]