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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 |
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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. |
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