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Symmetric semiclassical states to a magnetic nonlinear Schrödinger equation via equivariant Morse theory
An overview on some results concerning the transport equation and its applications to conservation laws
| 1. | Dipartimento di Matematica, Università degli Studi di Parma, viale G.P. Usberti 53/A (Campus), 43100 Parma |
| 2. | Centro De Giorgi, Collegio Puteano, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56126 Pisa, Italy |
| [1] |
Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic & Related Models, 2010, 3 (1) : 35-58. doi: 10.3934/krm.2010.3.35 |
| [2] |
María Santos Bruzón, Tamara María Garrido. Symmetries and conservation laws of a KdV6 equation. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 631-641. doi: 10.3934/dcdss.2018038 |
| [3] |
Zhi-Qiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure & Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759 |
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Stefano Bianchini, Daniela Tonon. A decomposition theorem for $BV$ functions. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1549-1566. doi: 10.3934/cpaa.2011.10.1549 |
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María Rosa, María de los Santos Bruzón, María de la Luz Gandarias. Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1331-1339. doi: 10.3934/dcdss.2015.8.1331 |
| [6] |
Avner Friedman. Conservation laws in mathematical biology. Discrete & Continuous Dynamical Systems, 2012, 32 (9) : 3081-3097. doi: 10.3934/dcds.2012.32.3081 |
| [7] |
Mauro Garavello. A review of conservation laws on networks. Networks & Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565 |
| [8] |
Len G. Margolin, Roy S. Baty. Conservation laws in discrete geometry. Journal of Geometric Mechanics, 2019, 11 (2) : 187-203. doi: 10.3934/jgm.2019010 |
| [9] |
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2007, 2 (1) : 159-179. doi: 10.3934/nhm.2007.2.159 |
| [10] |
Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044 |
| [11] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
| [12] |
Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure & Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755 |
| [13] |
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73 |
| [14] |
María-Santos Bruzón, Elena Recio, Tamara-María Garrido, Rafael de la Rosa. Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2691-2701. doi: 10.3934/dcdss.2020222 |
| [15] |
Giuseppe Maria Coclite, Lorenzo di Ruvo. A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation. Networks & Heterogeneous Media, 2016, 11 (2) : 281-300. doi: 10.3934/nhm.2016.11.281 |
| [16] |
Zhijie Cao, Lijun Zhang. Symmetries and conservation laws of a time dependent nonlinear reaction-convection-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2703-2717. doi: 10.3934/dcdss.2020218 |
| [17] |
Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 41-74. doi: 10.3934/dcdsb.2010.14.41 |
| [18] |
Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 75-109. doi: 10.3934/dcdsb.2010.14.75 |
| [19] |
Christophe Prieur. Control of systems of conservation laws with boundary errors. Networks & Heterogeneous Media, 2009, 4 (2) : 393-407. doi: 10.3934/nhm.2009.4.393 |
| [20] |
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
2020 Impact Factor: 1.916
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