-
Previous Article
Long-time behavior of a Bose-Einstein equation in a two-dimensional thin domain
- CPAA Home
- This Issue
-
Next Article
Vortex interaction dynamics in trapped Bose-Einstein condensates
A generalization of $H$-measures and application on purely fractional scalar conservation laws
1. | Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81000 Podgorica |
2. | Faculty of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia |
References:
[1] |
J. Aleksić, D. Mitrovíc and S. Pilipović, Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media, Journal of Evolution Equations, 9 (2009), 809-828.
doi: doi:10.1007/s00028-009-0035-5. |
[2] |
N. Alibaud, Entropy formulation for fractal conservation laws, Journal of Evolution Equations, 7 (2007), 145-175.
doi: doi:10.1007/s00028-006-0253-z. |
[3] |
N. Antonic and M. Lazar, Parabolic variant of H-measures in homogenisation of a model problem based on Navier-Stokes equation, Nonlinear Analysis-Real World Appl, 11 (2010), 4500-4512.
doi: doi:10.1016/j.nonrwa.2008.07.010. |
[4] |
N. Antonic and M. Lazar, $H$-measures and variants applied to parabolic equations, J. Math. Anal. Appl., 343 (2008), 207-225.
doi: doi:10.1016/j.jmaa.2007.12.077. |
[5] |
R. DiPerna, Compensated compactness and general systems of conservation laws, Trans. Amer. Math. Soc., 292 (1985), 383-419.
doi: doi:10.1090/S0002-9947-1985-0808729-4. |
[6] |
J. Droniou and C. Imbert, Fractal first-order partial differential equations, Arch. Ration. Mech. Anal., 182 (2006), 299-331.
doi: doi:10.1007/s00205-006-0429-2. |
[7] |
P. Gerard, Microlocal Defect Measures, Comm. Partial Differential Equations, 16 (1991), 1761-1794.
doi: doi:10.1080/03605309108820822. |
[8] |
S. N. Kruzhkov, First order quasilinear equations in several independent variables, Mat. Sbornik., 81 (1970), 228-255; English transl. in Math. USSR Sb., 10 (1970), 217-243. |
[9] |
P. L. Lions, B. Perthame and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. of American Math. Soc., 7 (1994), 169-191.
doi: doi:10.1090/S0894-0347-1994-1201239-3. |
[10] |
P. L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case, Part I. Ann. Inst. H. Poincare Sect. A (N.S.), 1 (1984), 109-145, 223-283. |
[11] |
P. L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case, Part II. Ann. Inst. H.Poincare Sect. A (N.S.), 1 (1984), 109-145, 223-283. |
[12] |
D. Mitrovic, Existence and stability of a multidimensional scalar conservation law with discontinuous flux, Netw. Het. Media, 5 (2010), 163-188.
doi: doi:10.3934/nhm.2010.5.163. |
[13] |
E. Yu. Panov, On sequences of measure-valued solutions of a first order quasilinear equations, Russian Acad. Sci. Sb. Math., 81 (1995), 211-227.
doi: doi:10.1070/SM1995v081n01ABEH003621. |
[14] |
E. Yu. Panov, Ultra-parabolic equations with rough coefficients. Entropy solutions and strong pre-compactness property, Journal of Mathematical Sciences, 159 (2009), 180-228.
doi: doi:10.1007/s10958-009-9434-y. |
[15] |
E. Yu. Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws, Journal of Hyperbolic Differential Equations, 4 (2007), 729-770.
doi: doi:10.1142/S0219891607001343. |
[16] |
E. Yu. Panov, Existence and strong precompactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux, Arch. Ration. Mech. Anal., 195 (2010), 643-673.
doi: doi:10.1007/s00205-009-0217-x. |
[17] |
S. A. Sazhenkov, The genuinely nonlinear Graetz-Nusselt ultraparabolic equation, (Russian. Russian summary) Sibirsk. Mat. Zh., 47 (2006), 431-454; translation in Siberian Math. J., 47 (2006), 355-375.
doi: doi:10.1007/s11202-006-0048-z. |
[18] |
L. Tartar, H-measures, a new approach for studying homogenisation, oscillation and concentration effects in PDEs, Proc. Roy. Soc. Edinburgh. Sect. A, 115 (1990), 193-230. |
[19] |
L. Tartar, "The General Theory of Homogenization. A Personalized Introduction," Lecture Notes of the Unione Matematica Italiana, 7. Springer-Verlag, Berlin; UMI, Bologna, 2009. xxii+470 pp. |
show all references
References:
[1] |
J. Aleksić, D. Mitrovíc and S. Pilipović, Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media, Journal of Evolution Equations, 9 (2009), 809-828.
doi: doi:10.1007/s00028-009-0035-5. |
[2] |
N. Alibaud, Entropy formulation for fractal conservation laws, Journal of Evolution Equations, 7 (2007), 145-175.
doi: doi:10.1007/s00028-006-0253-z. |
[3] |
N. Antonic and M. Lazar, Parabolic variant of H-measures in homogenisation of a model problem based on Navier-Stokes equation, Nonlinear Analysis-Real World Appl, 11 (2010), 4500-4512.
doi: doi:10.1016/j.nonrwa.2008.07.010. |
[4] |
N. Antonic and M. Lazar, $H$-measures and variants applied to parabolic equations, J. Math. Anal. Appl., 343 (2008), 207-225.
doi: doi:10.1016/j.jmaa.2007.12.077. |
[5] |
R. DiPerna, Compensated compactness and general systems of conservation laws, Trans. Amer. Math. Soc., 292 (1985), 383-419.
doi: doi:10.1090/S0002-9947-1985-0808729-4. |
[6] |
J. Droniou and C. Imbert, Fractal first-order partial differential equations, Arch. Ration. Mech. Anal., 182 (2006), 299-331.
doi: doi:10.1007/s00205-006-0429-2. |
[7] |
P. Gerard, Microlocal Defect Measures, Comm. Partial Differential Equations, 16 (1991), 1761-1794.
doi: doi:10.1080/03605309108820822. |
[8] |
S. N. Kruzhkov, First order quasilinear equations in several independent variables, Mat. Sbornik., 81 (1970), 228-255; English transl. in Math. USSR Sb., 10 (1970), 217-243. |
[9] |
P. L. Lions, B. Perthame and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. of American Math. Soc., 7 (1994), 169-191.
doi: doi:10.1090/S0894-0347-1994-1201239-3. |
[10] |
P. L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case, Part I. Ann. Inst. H. Poincare Sect. A (N.S.), 1 (1984), 109-145, 223-283. |
[11] |
P. L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case, Part II. Ann. Inst. H.Poincare Sect. A (N.S.), 1 (1984), 109-145, 223-283. |
[12] |
D. Mitrovic, Existence and stability of a multidimensional scalar conservation law with discontinuous flux, Netw. Het. Media, 5 (2010), 163-188.
doi: doi:10.3934/nhm.2010.5.163. |
[13] |
E. Yu. Panov, On sequences of measure-valued solutions of a first order quasilinear equations, Russian Acad. Sci. Sb. Math., 81 (1995), 211-227.
doi: doi:10.1070/SM1995v081n01ABEH003621. |
[14] |
E. Yu. Panov, Ultra-parabolic equations with rough coefficients. Entropy solutions and strong pre-compactness property, Journal of Mathematical Sciences, 159 (2009), 180-228.
doi: doi:10.1007/s10958-009-9434-y. |
[15] |
E. Yu. Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws, Journal of Hyperbolic Differential Equations, 4 (2007), 729-770.
doi: doi:10.1142/S0219891607001343. |
[16] |
E. Yu. Panov, Existence and strong precompactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux, Arch. Ration. Mech. Anal., 195 (2010), 643-673.
doi: doi:10.1007/s00205-009-0217-x. |
[17] |
S. A. Sazhenkov, The genuinely nonlinear Graetz-Nusselt ultraparabolic equation, (Russian. Russian summary) Sibirsk. Mat. Zh., 47 (2006), 431-454; translation in Siberian Math. J., 47 (2006), 355-375.
doi: doi:10.1007/s11202-006-0048-z. |
[18] |
L. Tartar, H-measures, a new approach for studying homogenisation, oscillation and concentration effects in PDEs, Proc. Roy. Soc. Edinburgh. Sect. A, 115 (1990), 193-230. |
[19] |
L. Tartar, "The General Theory of Homogenization. A Personalized Introduction," Lecture Notes of the Unione Matematica Italiana, 7. Springer-Verlag, Berlin; UMI, Bologna, 2009. xxii+470 pp. |
[1] |
Christophe Chalons, Paola Goatin, Nicolas Seguin. General constrained conservation laws. Application to pedestrian flow modeling. Networks and Heterogeneous Media, 2013, 8 (2) : 433-463. doi: 10.3934/nhm.2013.8.433 |
[2] |
Matthieu Brassart. Non-critical fractional conservation laws in domains with boundary. Networks and Heterogeneous Media, 2016, 11 (2) : 251-262. doi: 10.3934/nhm.2016.11.251 |
[3] |
Avner Friedman. Conservation laws in mathematical biology. Discrete and Continuous Dynamical Systems, 2012, 32 (9) : 3081-3097. doi: 10.3934/dcds.2012.32.3081 |
[4] |
Mauro Garavello. A review of conservation laws on networks. Networks and Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565 |
[5] |
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 |
[6] |
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2007, 2 (1) : 159-179. doi: 10.3934/nhm.2007.2.159 |
[7] |
Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044 |
[8] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
[9] |
Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure and Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755 |
[10] |
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73 |
[11] |
Christophe Prieur. Control of systems of conservation laws with boundary errors. Networks and Heterogeneous Media, 2009, 4 (2) : 393-407. doi: 10.3934/nhm.2009.4.393 |
[12] |
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
[13] |
Rinaldo M. Colombo, Kenneth H. Karlsen, Frédéric Lagoutière, Andrea Marson. Special issue on contemporary topics in conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : i-ii. doi: 10.3934/nhm.2016.11.2i |
[14] |
Boris Andreianov, Kenneth H. Karlsen, Nils H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2010, 5 (3) : 617-633. doi: 10.3934/nhm.2010.5.617 |
[15] |
Laurent Lévi, Julien Jimenez. Coupling of scalar conservation laws in stratified porous media. Conference Publications, 2007, 2007 (Special) : 644-654. doi: 10.3934/proc.2007.2007.644 |
[16] |
Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic and Related Models, 2010, 3 (1) : 35-58. doi: 10.3934/krm.2010.3.35 |
[17] |
Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301 |
[18] |
Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011 |
[19] |
Dmitry V. Zenkov. Linear conservation laws of nonholonomic systems with symmetry. Conference Publications, 2003, 2003 (Special) : 967-976. doi: 10.3934/proc.2003.2003.967 |
[20] |
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51 |
2021 Impact Factor: 1.273
Tools
Metrics
Other articles
by authors
[Back to Top]