-
Previous Article
Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method
- MBE Home
- This Issue
-
Next Article
Basic stage structure measure valued evolutionary game model
Stability and optimization in structured population models on graphs
| 1. | INdAM Unit, University of Brescia, Brescia |
| 2. | Department of Mathematics and Applications, University of Milano-Bicocca, Via R. Cozzi, 53, 20125 Milano |
- Abstract
- Related Papers
Under a Creative Commons license
References:
| [1] |
A. S. Ackleh and K. Deng, A nonautonomous juvenile-adult model: Well-posedness and long-time behavior via a comparison principle, SIAM J. Appl. Math., 69 (2009), 1644-1661.
doi: 10.1137/080723673. |
| [2] |
A. S. Ackleh, K. Deng and X. Yang, Sensitivity analysis for a structured juvenile-adult model, Comput. Math. Appl., 64 (2012), 190-200.
doi: 10.1016/j.camwa.2011.12.053. |
| [3] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 2000. |
| [4] |
C. Bardos, A. Y. le Roux and J.-C. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, 4 (1979), 1017-1034.
doi: 10.1080/03605307908820117. |
| [5] |
F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Second edition, Texts in Applied Mathematics, 40, Springer, New York, 2012.
doi: 10.1007/978-1-4614-1686-9. |
| [6] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem, Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
| [7] |
J. A. Carrillo, S. Cuadrado and B. Perthame, Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model, Math. Biosci., 205 (2007), 137-161.
doi: 10.1016/j.mbs.2006.09.012. |
| [8] |
R. M. Colombo and G. Guerra, On general balance laws with boundary, J. Differential Equations, 248 (2010), 1017-1043.
doi: 10.1016/j.jde.2009.12.002. |
| [9] |
R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Optimal control in networks of pipes and canals, SIAM J. Control Optim., 48 (2009), 2032-2050.
doi: 10.1137/080716372. |
| [10] |
M. Garavello and B. Piccoli, Traffic Flow on Networks, AIMS Series on Applied Mathematics, 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006. |
| [11] |
N. Keyfitz, The mathematics of sex and marriage, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 4: Biology and Health, University of California Press, Berkeley, Calif., 1972, 89-108. |
| [12] |
S. N. Kružhkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81 (1970), 228-255. |
| [13] |
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002.
doi: 10.1017/CBO9780511791253. |
| [14] |
P. Manfredi, Logistic effects in the two-sex model with "harmonic mean" fertility function, Genus, 49 (1993), 43-65. |
| [15] |
B. Perthame, Transport Equations in Biology, Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2007. |
| [16] |
R. Schoen, The harmonic mean as the basis of a realistic two-sex marriage model, Demography, 18 (1981), 201-216.
doi: 10.2307/2061093. |
| [17] |
R. Schoen, Relationships in a simple harmonic mean two-sex fertility model, Journal of Mathematical Biology, 18 (1983), 201-211.
doi: 10.1007/BF00276087. |
| [18] |
R. Schoen, Modeling Multigroup Populations, Springer, 1988.
doi: 10.1007/978-1-4899-2055-3. |
| [19] |
D. Serre, Systems of Conservation Laws. 2. Geometric Structures, Oscillations, and Initial-Boundary Value Problems, Translated from the 1996 French original by I. N. Sneddon, Cambridge University Press, Cambridge, 2000. |
| [20] |
A. Sundelof and P. Aberg, Birth functions in stage structured two-sex models, Ecological Modeling, 193 (2006), 787-795.
doi: 10.1016/j.ecolmodel.2005.08.040. |
show all references
References:
| [1] |
A. S. Ackleh and K. Deng, A nonautonomous juvenile-adult model: Well-posedness and long-time behavior via a comparison principle, SIAM J. Appl. Math., 69 (2009), 1644-1661.
doi: 10.1137/080723673. |
| [2] |
A. S. Ackleh, K. Deng and X. Yang, Sensitivity analysis for a structured juvenile-adult model, Comput. Math. Appl., 64 (2012), 190-200.
doi: 10.1016/j.camwa.2011.12.053. |
| [3] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 2000. |
| [4] |
C. Bardos, A. Y. le Roux and J.-C. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, 4 (1979), 1017-1034.
doi: 10.1080/03605307908820117. |
| [5] |
F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Second edition, Texts in Applied Mathematics, 40, Springer, New York, 2012.
doi: 10.1007/978-1-4614-1686-9. |
| [6] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem, Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
| [7] |
J. A. Carrillo, S. Cuadrado and B. Perthame, Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model, Math. Biosci., 205 (2007), 137-161.
doi: 10.1016/j.mbs.2006.09.012. |
| [8] |
R. M. Colombo and G. Guerra, On general balance laws with boundary, J. Differential Equations, 248 (2010), 1017-1043.
doi: 10.1016/j.jde.2009.12.002. |
| [9] |
R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Optimal control in networks of pipes and canals, SIAM J. Control Optim., 48 (2009), 2032-2050.
doi: 10.1137/080716372. |
| [10] |
M. Garavello and B. Piccoli, Traffic Flow on Networks, AIMS Series on Applied Mathematics, 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006. |
| [11] |
N. Keyfitz, The mathematics of sex and marriage, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 4: Biology and Health, University of California Press, Berkeley, Calif., 1972, 89-108. |
| [12] |
S. N. Kružhkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81 (1970), 228-255. |
| [13] |
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002.
doi: 10.1017/CBO9780511791253. |
| [14] |
P. Manfredi, Logistic effects in the two-sex model with "harmonic mean" fertility function, Genus, 49 (1993), 43-65. |
| [15] |
B. Perthame, Transport Equations in Biology, Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2007. |
| [16] |
R. Schoen, The harmonic mean as the basis of a realistic two-sex marriage model, Demography, 18 (1981), 201-216.
doi: 10.2307/2061093. |
| [17] |
R. Schoen, Relationships in a simple harmonic mean two-sex fertility model, Journal of Mathematical Biology, 18 (1983), 201-211.
doi: 10.1007/BF00276087. |
| [18] |
R. Schoen, Modeling Multigroup Populations, Springer, 1988.
doi: 10.1007/978-1-4899-2055-3. |
| [19] |
D. Serre, Systems of Conservation Laws. 2. Geometric Structures, Oscillations, and Initial-Boundary Value Problems, Translated from the 1996 French original by I. N. Sneddon, Cambridge University Press, Cambridge, 2000. |
| [20] |
A. Sundelof and P. Aberg, Birth functions in stage structured two-sex models, Ecological Modeling, 193 (2006), 787-795.
doi: 10.1016/j.ecolmodel.2005.08.040. |
| [1] |
Azmy S. Ackleh, Keng Deng. Stability of a delay equation arising from a juvenile-adult model. Mathematical Biosciences & Engineering, 2010, 7 (4) : 729-737. doi: 10.3934/mbe.2010.7.729 |
| [2] |
J. M. Cushing, Simon Maccracken Stump. Darwinian dynamics of a juvenile-adult model. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1017-1044. doi: 10.3934/mbe.2013.10.1017 |
| [3] |
Xianlong Fu, Dongmei Zhu. Stability analysis for a size-structured juvenile-adult population model. Discrete and Continuous Dynamical Systems - B, 2014, 19 (2) : 391-417. doi: 10.3934/dcdsb.2014.19.391 |
| [4] |
Azmy S. Ackleh, Keng Deng, Qihua Huang. Difference approximation for an amphibian juvenile-adult dispersal mode. Conference Publications, 2011, 2011 (Special) : 1-12. doi: 10.3934/proc.2011.2011.1 |
| [5] |
József Z. Farkas, Thomas Hagen. Asymptotic behavior of size-structured populations via juvenile-adult interaction. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 249-266. doi: 10.3934/dcdsb.2008.9.249 |
| [6] |
Jumpei Inoue, Kousuke Kuto. On the unboundedness of the ratio of species and resources for the diffusive logistic equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2441-2450. doi: 10.3934/dcdsb.2020186 |
| [7] |
Constantine M. Dafermos. Hyperbolic balance laws with relaxation. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4271-4285. doi: 10.3934/dcds.2016.36.4271 |
| [8] |
Georgios I. Papayiannis. Robust policy selection and harvest risk quantification for natural resources management under model uncertainty. Journal of Dynamics and Games, 2022, 9 (2) : 203-217. doi: 10.3934/jdg.2022004 |
| [9] |
Prabir Panja, Soovoojeet Jana, Shyamal kumar Mondal. Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey. Numerical Algebra, Control and Optimization, 2021, 11 (3) : 391-405. doi: 10.3934/naco.2020033 |
| [10] |
Graziano Crasta, Benedetto Piccoli. Viscosity solutions and uniqueness for systems of inhomogeneous balance laws. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 477-502. doi: 10.3934/dcds.1997.3.477 |
| [11] |
Rinaldo M. Colombo, Graziano Guerra. Hyperbolic balance laws with a dissipative non local source. Communications on Pure and Applied Analysis, 2008, 7 (5) : 1077-1090. doi: 10.3934/cpaa.2008.7.1077 |
| [12] |
Laura Caravenna. Regularity estimates for continuous solutions of α-convex balance laws. Communications on Pure and Applied Analysis, 2017, 16 (2) : 629-644. doi: 10.3934/cpaa.2017031 |
| [13] |
Xing Liang, Lei Zhang. The optimal distribution of resources and rate of migration maximizing the population size in logistic model with identical migration. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2055-2065. doi: 10.3934/dcdsb.2020280 |
| [14] |
Ryszard Rudnicki, Radoslaw Wieczorek. Does assortative mating lead to a polymorphic population? A toy model justification. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 459-472. doi: 10.3934/dcdsb.2018031 |
| [15] |
Alessia Marigo, Benedetto Piccoli. A model for biological dynamic networks. Networks and Heterogeneous Media, 2011, 6 (4) : 647-663. doi: 10.3934/nhm.2011.6.647 |
| [16] |
Linhao Xu, Marya Claire Zdechlik, Melissa C. Smith, Min B. Rayamajhi, Don L. DeAngelis, Bo Zhang. Simulation of post-hurricane impact on invasive species with biological control management. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 4059-4071. doi: 10.3934/dcds.2020038 |
| [17] |
Yanni Zeng. LP decay for general hyperbolic-parabolic systems of balance laws. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 363-396. doi: 10.3934/dcds.2018018 |
| [18] |
Piotr Gwiazda, Piotr Orlinski, Agnieszka Ulikowska. Finite range method of approximation for balance laws in measure spaces. Kinetic and Related Models, 2017, 10 (3) : 669-688. doi: 10.3934/krm.2017027 |
| [19] |
Stephan Gerster, Michael Herty. Discretized feedback control for systems of linearized hyperbolic balance laws. Mathematical Control and Related Fields, 2019, 9 (3) : 517-539. doi: 10.3934/mcrf.2019024 |
| [20] |
Kenta Nakamura, Tohru Nakamura, Shuichi Kawashima. Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws. Kinetic and Related Models, 2019, 12 (4) : 923-944. doi: 10.3934/krm.2019035 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]