September  2008, 7(5): 1077-1090. doi: 10.3934/cpaa.2008.7.1077

Hyperbolic balance laws with a dissipative non local source

1. 

Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy

2. 

Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8 – 20126 Milano, Italy

Received  October 2007 Revised  March 2008 Published  June 2008

This paper considers systems of balance law with a dissipative non local source. A global in time well posedness result is obtained. Estimates on the dependence of solutions from the flow and from the source term are also provided. The technique relies on a recent result on quasidifferential equations in metric spaces.
Citation: Rinaldo M. Colombo, Graziano Guerra. Hyperbolic balance laws with a dissipative non local source. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1077-1090. doi: 10.3934/cpaa.2008.7.1077
[1]

Constantine M. Dafermos. Hyperbolic balance laws with relaxation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4271-4285. doi: 10.3934/dcds.2016.36.4271

[2]

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

[3]

Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143

[4]

Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673

[5]

Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011

[6]

Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure & Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51

[7]

Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 717-731. doi: 10.3934/nhm.2007.2.717

[8]

Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185

[9]

Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 15-32. doi: 10.3934/dcdss.2016.9.15

[10]

Yanni Zeng. LP decay for general hyperbolic-parabolic systems of balance laws. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 363-396. doi: 10.3934/dcds.2018018

[11]

Stephan Gerster, Michael Herty. Discretized feedback control for systems of linearized hyperbolic balance laws. Mathematical Control & Related Fields, 2019, 9 (3) : 517-539. doi: 10.3934/mcrf.2019024

[12]

Kenta Nakamura, Tohru Nakamura, Shuichi Kawashima. Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws. Kinetic & Related Models, 2019, 12 (4) : 923-944. doi: 10.3934/krm.2019035

[13]

Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control & Related Fields, 2013, 3 (2) : 121-142. doi: 10.3934/mcrf.2013.3.121

[14]

Eitan Tadmor. Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4579-4598. doi: 10.3934/dcds.2016.36.4579

[15]

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

[16]

Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 597-609. doi: 10.3934/dcds.2006.15.597

[17]

Boris Andreianov, Mohamed Karimou Gazibo. Explicit formulation for the Dirichlet problem for parabolic-hyperbolic conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 203-222. doi: 10.3934/nhm.2016.11.203

[18]

Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073

[19]

Avner Friedman. Conservation laws in mathematical biology. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3081-3097. doi: 10.3934/dcds.2012.32.3081

[20]

Mauro Garavello. A review of conservation laws on networks. Networks & Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]