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Conservation laws with discontinuous flux
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Existence and stability of entropy solutions for a conservation law with discontinuous nonconvex fluxes
1.  Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Post Bag No 6503, Sharadanagar, Bangalore  560065, India 
2.  Center of Mathematics for Applications, University of Oslo, P.O. Box 1053, Oslo, Norway 
3.  TIFR center, IISc Campus, P.O. Box 1234, Bangalore, India 
[1] 
Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra. Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks & Heterogeneous Media, 2013, 8 (4) : 969984. doi: 10.3934/nhm.2013.8.969 
[2] 
Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete & Continuous Dynamical Systems  A, 2011, 30 (4) : 11911210. doi: 10.3934/dcds.2011.30.1191 
[3] 
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2007, 2 (1) : 159179. doi: 10.3934/nhm.2007.2.159 
[4] 
Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 349367. doi: 10.3934/nhm.2016.11.349 
[5] 
YoungSam Kwon. On the wellposedness of entropy solutions for conservation laws with source terms. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 933949. doi: 10.3934/dcds.2009.25.933 
[6] 
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 7388. doi: 10.3934/dcdss.2016.9.73 
[7] 
Boris Andreianov, Kenneth H. Karlsen, Nils H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 617633. doi: 10.3934/nhm.2010.5.617 
[8] 
ZhiQiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initialboundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure & Applied Analysis, 2015, 14 (3) : 759792. doi: 10.3934/cpaa.2015.14.759 
[9] 
JoãoPaulo Dias, Mário Figueira. On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions. Communications on Pure & Applied Analysis, 2004, 3 (1) : 5358. doi: 10.3934/cpaa.2004.3.53 
[10] 
Eitan Tadmor. Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws. Discrete & Continuous Dynamical Systems  A, 2016, 36 (8) : 45794598. doi: 10.3934/dcds.2016.36.4579 
[11] 
GuiQiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure & Applied Analysis, 2011, 10 (4) : 10111036. doi: 10.3934/cpaa.2011.10.1011 
[12] 
C. M. Khalique, G. S. Pai. Conservation laws and invariant solutions for soil water equations. Conference Publications, 2003, 2003 (Special) : 477481. doi: 10.3934/proc.2003.2003.477 
[13] 
Raimund Bürger, Kenneth H. Karlsen, John D. Towers. On some difference schemes and entropy conditions for a class of multispecies kinematic flow models with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 461485. doi: 10.3934/nhm.2010.5.461 
[14] 
Boris P. Andreianov, Giuseppe Maria Coclite, Carlotta Donadello. Wellposedness for vanishing viscosity solutions of scalar conservation laws on a network. Discrete & Continuous Dynamical Systems  A, 2017, 37 (11) : 59135942. doi: 10.3934/dcds.2017257 
[15] 
Fengbai Li, Feng Rong. Decay of solutions to fractal parabolic conservation laws with large initial data. Communications on Pure & Applied Analysis, 2013, 12 (2) : 973984. doi: 10.3934/cpaa.2013.12.973 
[16] 
Shijin Deng, Weike Wang. Pointwise estimates of solutions for the multidimensional scalar conservation laws with relaxation. Discrete & Continuous Dynamical Systems  A, 2011, 30 (4) : 11071138. doi: 10.3934/dcds.2011.30.1107 
[17] 
Lijuan Wang, Weike Wang. Pointwise estimates of solutions to conservation laws with nonlocal dissipationtype terms. Communications on Pure & Applied Analysis, 2019, 18 (5) : 28352854. doi: 10.3934/cpaa.2019127 
[18] 
Avner Friedman. Conservation laws in mathematical biology. Discrete & Continuous Dynamical Systems  A, 2012, 32 (9) : 30813097. doi: 10.3934/dcds.2012.32.3081 
[19] 
Mauro Garavello. A review of conservation laws on networks. Networks & Heterogeneous Media, 2010, 5 (3) : 565581. doi: 10.3934/nhm.2010.5.565 
[20] 
Len G. Margolin, Roy S. Baty. Conservation laws in discrete geometry. Journal of Geometric Mechanics, 2019, 11 (2) : 187203. doi: 10.3934/jgm.2019010 
2018 Impact Factor: 0.871
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