-
Previous Article
Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings
- NHM Home
- This Issue
- Next Article
Asymptotic periodicity of flows in time-depending networks
1. | Universität Tübingen, Mathematisch-Naturwissenschaftliche Fakultät, Auf der Morgenstelle 10, D-72076 Tübingen |
2. | WSI für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany |
3. | University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia |
References:
[1] |
F. Bayazit, Positive evolution families solving nonautonomous difference equations, Positivity, 16 (2012), 653-684.
doi: 10.1007/s11117-011-0139-3. |
[2] |
F. Bayazit, On the Asymptotic Behavior of Periodic Evolution Families on Banach Spaces, Ph.D thesis, Eberhard Karls Universität Tübingen, 2012. |
[3] |
A. M. Bayen, R. L. Raffard and C. L. Tomlin, Eulerian network model of air traffic flow in congested areas, Proc. of the American Control Conference, (2004), 5520-5526. |
[4] |
A. M. Bayen, R. L. Raffard and C. L. Tomlin, Adjoint-based control of Eulerian transportation networks: application to air traffic control, Proc. of the American Control Conference, (2004), 5539-5545. |
[5] |
A. M. Bayen, R. L. Raffard and C. L. Tomlin, Adjoint-based control of a new Eulerian network model of air traffic flow, IEEE Transactions on Control Systems Technology, 14 (2006), 804-818.
doi: 10.1109/TCST.2006.876904. |
[6] |
B. Dorn, Semigroups for flows in infinite networks, Semigroup Forum, 76 (2008), 341-356.
doi: 10.1007/s00233-007-9036-2. |
[7] |
B. Dorn, Flows in Infinite Networks - A Semigroup Approach, Ph.D thesis, Eberhard Karls Universität Tübingen, 2008. |
[8] |
B. Dorn, V. Keicher and E. Sikolya, Asymptotic periodicity of recurrent flows in infinite networks, Math. Z., 263 (2009), 69-87.
doi: 10.1007/s00209-008-0410-x. |
[9] |
B. Dorn, M. Kramar Fijavž, R. Nagel and A. Radl, The semigroup approach to flows in networks, Physica D, 239 (2010), 1416-1421.
doi: 10.1016/j.physd.2009.06.012. |
[10] |
K.-J. Engel, M. Kramar Fijavž, B. Klöss, R. Nagel and E. Sikolya, Maximal controllability for boundary control problems, Appl. Math. Optim., 62 (2010), 205-227.
doi: 10.1007/s00245-010-9101-1. |
[11] |
K.-J. Engel, M. Kramar Fijavž, R. Nagel and E. Sikolya, Vertex control of flows in networks, J. Networks Heterogeneous Media, 3 (2008), 709-722.
doi: 10.3934/nhm.2008.3.709. |
[12] |
K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Math. 194, Springer-Verlag, 2000. |
[13] |
M. Garavello and B. Piccoli, Traffic Flow on Networks, American Institute of Mathematical Sciences, 2006. |
[14] |
M. Kramar and E. Sikolya, Spectral properties and asymptotic periodicity of flows in networks, Math. Z., 249 (2005), 139-162.
doi: 10.1007/s00209-004-0695-3. |
[15] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. of the Royal Society of London, 229 (1956), 317-345.
doi: 10.1098/rspa.1955.0089. |
[16] |
T. Mátrai and E. Sikolya, Asymptotic behavior of flows in networks, Forum Math., 19 (2007), 429-461.
doi: 10.1515/FORUM.2007.018. |
[17] |
P. K. Menon, G. D. Sweriduk and K. Bilimoria, A new approach for modeling, analysis and control of air traffic flow, AIAA Journal of Guidance, Control and Dynamics, 27 (2004), 737-744. |
[18] | |
[19] |
R. Nagel, Semigroup methods for nonautonomous Cauchy problems, Evolution Equations, Lecture Notes in Pure and Appl. Math., 168 (1995), 301-316. |
[20] |
R. Nagel and G. Nickel, Well-posedness for nonautonomous abstract Cauchy problems, Prog. Nonlinear Differential Equations Appl., 50 (2002), 279-293. |
[21] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[22] |
A. Radl, Transport processes in networks with scattering ramification nodes, J. Appl. Funct. Anal., 3 (2008), 461-483. |
[23] |
P. I. Richards, Shock waves on the highway, Oper. Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[24] |
C.-A. Robelin, D. Sun, G. Wu and A. M. Bayen, MILP control of aggregate Eulerian network airspace models, Proc. of the American Control Conference, (2006), 5257-5262.
doi: 10.1109/ACC.2006.1657558. |
[25] |
H. H. Schaefer, Banach Lattices and Positive Operators, Grundlehren Math. Wiss., 215, Springer-Verlag, 1974. |
[26] |
E. Sikolya, Flows in networks with dynamic ramification nodes, J. Evol. Equ., 5 (2005), 441-463.
doi: 10.1007/s00028-005-0221-z. |
[27] |
B. Sridhar and P. K. Menon, Comparison of linear dynamic models for air traffic flow management, Proc. 16th IFAC World Congress, (2005). |
[28] |
D. Sun, I. S. Strub and A. M. Bayen, Comparison of the performance of four Eulerian network flow models for strategic air traffic management, Netw. Heterog. Media, 2 (2007), 569-595.
doi: 10.3934/nhm.2007.2.569. |
show all references
References:
[1] |
F. Bayazit, Positive evolution families solving nonautonomous difference equations, Positivity, 16 (2012), 653-684.
doi: 10.1007/s11117-011-0139-3. |
[2] |
F. Bayazit, On the Asymptotic Behavior of Periodic Evolution Families on Banach Spaces, Ph.D thesis, Eberhard Karls Universität Tübingen, 2012. |
[3] |
A. M. Bayen, R. L. Raffard and C. L. Tomlin, Eulerian network model of air traffic flow in congested areas, Proc. of the American Control Conference, (2004), 5520-5526. |
[4] |
A. M. Bayen, R. L. Raffard and C. L. Tomlin, Adjoint-based control of Eulerian transportation networks: application to air traffic control, Proc. of the American Control Conference, (2004), 5539-5545. |
[5] |
A. M. Bayen, R. L. Raffard and C. L. Tomlin, Adjoint-based control of a new Eulerian network model of air traffic flow, IEEE Transactions on Control Systems Technology, 14 (2006), 804-818.
doi: 10.1109/TCST.2006.876904. |
[6] |
B. Dorn, Semigroups for flows in infinite networks, Semigroup Forum, 76 (2008), 341-356.
doi: 10.1007/s00233-007-9036-2. |
[7] |
B. Dorn, Flows in Infinite Networks - A Semigroup Approach, Ph.D thesis, Eberhard Karls Universität Tübingen, 2008. |
[8] |
B. Dorn, V. Keicher and E. Sikolya, Asymptotic periodicity of recurrent flows in infinite networks, Math. Z., 263 (2009), 69-87.
doi: 10.1007/s00209-008-0410-x. |
[9] |
B. Dorn, M. Kramar Fijavž, R. Nagel and A. Radl, The semigroup approach to flows in networks, Physica D, 239 (2010), 1416-1421.
doi: 10.1016/j.physd.2009.06.012. |
[10] |
K.-J. Engel, M. Kramar Fijavž, B. Klöss, R. Nagel and E. Sikolya, Maximal controllability for boundary control problems, Appl. Math. Optim., 62 (2010), 205-227.
doi: 10.1007/s00245-010-9101-1. |
[11] |
K.-J. Engel, M. Kramar Fijavž, R. Nagel and E. Sikolya, Vertex control of flows in networks, J. Networks Heterogeneous Media, 3 (2008), 709-722.
doi: 10.3934/nhm.2008.3.709. |
[12] |
K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Math. 194, Springer-Verlag, 2000. |
[13] |
M. Garavello and B. Piccoli, Traffic Flow on Networks, American Institute of Mathematical Sciences, 2006. |
[14] |
M. Kramar and E. Sikolya, Spectral properties and asymptotic periodicity of flows in networks, Math. Z., 249 (2005), 139-162.
doi: 10.1007/s00209-004-0695-3. |
[15] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. of the Royal Society of London, 229 (1956), 317-345.
doi: 10.1098/rspa.1955.0089. |
[16] |
T. Mátrai and E. Sikolya, Asymptotic behavior of flows in networks, Forum Math., 19 (2007), 429-461.
doi: 10.1515/FORUM.2007.018. |
[17] |
P. K. Menon, G. D. Sweriduk and K. Bilimoria, A new approach for modeling, analysis and control of air traffic flow, AIAA Journal of Guidance, Control and Dynamics, 27 (2004), 737-744. |
[18] | |
[19] |
R. Nagel, Semigroup methods for nonautonomous Cauchy problems, Evolution Equations, Lecture Notes in Pure and Appl. Math., 168 (1995), 301-316. |
[20] |
R. Nagel and G. Nickel, Well-posedness for nonautonomous abstract Cauchy problems, Prog. Nonlinear Differential Equations Appl., 50 (2002), 279-293. |
[21] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[22] |
A. Radl, Transport processes in networks with scattering ramification nodes, J. Appl. Funct. Anal., 3 (2008), 461-483. |
[23] |
P. I. Richards, Shock waves on the highway, Oper. Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[24] |
C.-A. Robelin, D. Sun, G. Wu and A. M. Bayen, MILP control of aggregate Eulerian network airspace models, Proc. of the American Control Conference, (2006), 5257-5262.
doi: 10.1109/ACC.2006.1657558. |
[25] |
H. H. Schaefer, Banach Lattices and Positive Operators, Grundlehren Math. Wiss., 215, Springer-Verlag, 1974. |
[26] |
E. Sikolya, Flows in networks with dynamic ramification nodes, J. Evol. Equ., 5 (2005), 441-463.
doi: 10.1007/s00028-005-0221-z. |
[27] |
B. Sridhar and P. K. Menon, Comparison of linear dynamic models for air traffic flow management, Proc. 16th IFAC World Congress, (2005). |
[28] |
D. Sun, I. S. Strub and A. M. Bayen, Comparison of the performance of four Eulerian network flow models for strategic air traffic management, Netw. Heterog. Media, 2 (2007), 569-595.
doi: 10.3934/nhm.2007.2.569. |
[1] |
Pengyu Chen, Yongxiang Li, Xuping Zhang. Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1531-1547. doi: 10.3934/dcdsb.2020171 |
[2] |
A. Marigo, Benedetto Piccoli. Cooperative controls for air traffic management. Communications on Pure and Applied Analysis, 2003, 2 (3) : 355-369. doi: 10.3934/cpaa.2003.2.355 |
[3] |
Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez, Miguel E. Vázquez-Méndez. Optimal control of urban air pollution related to traffic flow in road networks. Mathematical Control and Related Fields, 2018, 8 (1) : 177-193. doi: 10.3934/mcrf.2018008 |
[4] |
Pengyu Chen, Xuping Zhang. Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations. Evolution Equations and Control Theory, 2021, 10 (3) : 471-489. doi: 10.3934/eect.2020076 |
[5] |
K. Ravikumar, Manil T. Mohan, A. Anguraj. Approximate controllability of a non-autonomous evolution equation in Banach spaces. Numerical Algebra, Control and Optimization, 2021, 11 (3) : 461-485. doi: 10.3934/naco.2020038 |
[6] |
Mary Luz Mouronte, Rosa María Benito. Structural analysis and traffic flow in the transport networks of Madrid. Networks and Heterogeneous Media, 2015, 10 (1) : 127-148. doi: 10.3934/nhm.2015.10.127 |
[7] |
Sebastian Engel, Karl Kunisch. Optimal control of the linear wave equation by time-depending BV-controls: A semi-smooth Newton approach. Mathematical Control and Related Fields, 2020, 10 (3) : 591-622. doi: 10.3934/mcrf.2020012 |
[8] |
Mustapha Mokhtar-Kharroubi. On permanent regimes for non-autonomous linear evolution equations in Banach spaces with applications to transport theory. Kinetic and Related Models, 2010, 3 (3) : 473-499. doi: 10.3934/krm.2010.3.473 |
[9] |
Yacine Chitour, Guilherme Mazanti, Mario Sigalotti. Stability of non-autonomous difference equations with applications to transport and wave propagation on networks. Networks and Heterogeneous Media, 2016, 11 (4) : 563-601. doi: 10.3934/nhm.2016010 |
[10] |
Abdelaziz Rhandi, Roland Schnaubelt. Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 663-683. doi: 10.3934/dcds.1999.5.663 |
[11] |
Dengfeng Sun, Issam S. Strub, Alexandre M. Bayen. Comparison of the performance of four Eulerian network flow models for strategic air traffic management. Networks and Heterogeneous Media, 2007, 2 (4) : 569-595. doi: 10.3934/nhm.2007.2.569 |
[12] |
Tomás Caraballo, Antonio M. Márquez-Durán, Rivero Felipe. Asymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristic. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1817-1833. doi: 10.3934/dcdsb.2017108 |
[13] |
Lingyu Li, Zhang Chen. Asymptotic behavior of non-autonomous random Ginzburg-Landau equation driven by colored noise. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3303-3333. doi: 10.3934/dcdsb.2020233 |
[14] |
Felipe Rivero. Time dependent perturbation in a non-autonomous non-classical parabolic equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 209-221. doi: 10.3934/dcdsb.2013.18.209 |
[15] |
Yanan Li, Alexandre N. Carvalho, Tito L. M. Luna, Estefani M. Moreira. A non-autonomous bifurcation problem for a non-local scalar one-dimensional parabolic equation. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5181-5196. doi: 10.3934/cpaa.2020232 |
[16] |
Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17 |
[17] |
Mahesh G. Nerurkar. Spectral and stability questions concerning evolution of non-autonomous linear systems. Conference Publications, 2001, 2001 (Special) : 270-275. doi: 10.3934/proc.2001.2001.270 |
[18] |
Pengyu Chen. Periodic solutions to non-autonomous evolution equations with multi-delays. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 2921-2939. doi: 10.3934/dcdsb.2020211 |
[19] |
Peter E. Kloeden, Jacson Simsen. Pullback attractors for non-autonomous evolution equations with spatially variable exponents. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2543-2557. doi: 10.3934/cpaa.2014.13.2543 |
[20] |
Sylvia Novo, Rafael Obaya, Ana M. Sanz. Exponential stability in non-autonomous delayed equations with applications to neural networks. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 517-536. doi: 10.3934/dcds.2007.18.517 |
2020 Impact Factor: 1.213
Tools
Metrics
Other articles
by authors
[Back to Top]