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Asymptotic behaviour of flows on reducible networks
1. | School of Mathematical Sciences, UKZN, Durban |
2. | School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa |
References:
[1] |
W. J. Anderson, Continuous-Time Markov Chains. An Application Oriented Approach, Springer Verlag, New York, 1991.
doi: 10.1007/978-1-4612-3038-0. |
[2] |
W. Arendt, Resolvent positive operators, Proc. Lond. Math. Soc., 54 (1987), 321-349.
doi: 10.1112/plms/s3-54.2.321. |
[3] |
J. Banasiak and L. Arlotti, Perturbation of Positive Semigroups with Applications, Springer Verlag, London, 2006. |
[4] |
J. Banasiak and P. Namayanja, Relative entropy and discrete Poincaré inequalities for reducible matrices, Appl. Math. Lett., 25 (2012), 2193-2197.
doi: 10.1016/j.aml.2012.06.001. |
[5] |
J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications, 2nd ed., Springer Verlag, London, 2009.
doi: 10.1007/978-1-84800-998-1. |
[6] |
N. Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall, Inc., Englewood Cliffs, 1974. |
[7] |
B. Dorn, Flows in Infinite Networks - A Semigroup Aproach, Ph.D thesis, University of Tübingen, 2008. |
[8] |
B. Dorn, Semigroups for flows in infinite networks, Semigroup Forum, 76 (2008), 341-356.
doi: 10.1007/s00233-007-9036-2. |
[9] |
B. Dorn, M. Kramar Fijavž, R. Nagel and A. Radl, The semigroup approach to transport processes in networks, Physica D, 239 (2010), 1416-1421.
doi: 10.1016/j.physd.2009.06.012. |
[10] |
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. |
[11] |
K.-J. Engel and R. Nagel, One Parameter Semigroups for Linear Evolution Equations, Springer Verlag, New York, 2000. |
[12] |
F. R. Gantmacher, Applications of the Theory of Matrices, Interscience Publishers, Inc. New York, 1959. |
[13] |
Ch. Godsil and G. Royle, Algebraic Graph Theory, Springer Verlag, New York, 2001.
doi: 10.1007/978-1-4613-0163-9. |
[14] |
F.M. Hante, G. Leugering and T. I. Seidman, Modeling and analysis of modal switching in networked transport systems, Appl. Math. & Optimization, 59 (2009), 275-292.
doi: 10.1007/s00245-008-9057-6. |
[15] |
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. |
[16] |
T. Matrai and E. Sikolya, Asymptotic behaviour of flows in networks, Forum Math., 19 (2007), 429-461.
doi: 10.1515/FORUM.2007.018. |
[17] |
C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, 2000.
doi: 10.1137/1.9780898719512. |
[18] |
H. Minc, Nonnegative Matrices, John Wiley & Sons, New York, 1988. |
[19] |
R. Nagel, ed., One-parameter Semigroups of Positive Operators, Springer Verlag, Berlin, 1986. |
[20] |
P. Namayanja, Transport on Network Structures, Ph.D thesis, UKZN, 2012. |
[21] |
E. Seneta, Nonnegative Matrices and Markov Chains, Springer Verlag, New York, 1981.
doi: 10.1007/0-387-32792-4. |
[22] |
E. Sikolya, Semigroups for Flows in Networks, Ph.D dissertation, University of Tübingen, 2004. |
[23] |
E. Sikolya, Flows in networks with dynamic ramification nodes, J. Evol. Equ., 5 (2005), 441-463.
doi: 10.1007/s00028-005-0221-z. |
show all references
References:
[1] |
W. J. Anderson, Continuous-Time Markov Chains. An Application Oriented Approach, Springer Verlag, New York, 1991.
doi: 10.1007/978-1-4612-3038-0. |
[2] |
W. Arendt, Resolvent positive operators, Proc. Lond. Math. Soc., 54 (1987), 321-349.
doi: 10.1112/plms/s3-54.2.321. |
[3] |
J. Banasiak and L. Arlotti, Perturbation of Positive Semigroups with Applications, Springer Verlag, London, 2006. |
[4] |
J. Banasiak and P. Namayanja, Relative entropy and discrete Poincaré inequalities for reducible matrices, Appl. Math. Lett., 25 (2012), 2193-2197.
doi: 10.1016/j.aml.2012.06.001. |
[5] |
J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications, 2nd ed., Springer Verlag, London, 2009.
doi: 10.1007/978-1-84800-998-1. |
[6] |
N. Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall, Inc., Englewood Cliffs, 1974. |
[7] |
B. Dorn, Flows in Infinite Networks - A Semigroup Aproach, Ph.D thesis, University of Tübingen, 2008. |
[8] |
B. Dorn, Semigroups for flows in infinite networks, Semigroup Forum, 76 (2008), 341-356.
doi: 10.1007/s00233-007-9036-2. |
[9] |
B. Dorn, M. Kramar Fijavž, R. Nagel and A. Radl, The semigroup approach to transport processes in networks, Physica D, 239 (2010), 1416-1421.
doi: 10.1016/j.physd.2009.06.012. |
[10] |
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. |
[11] |
K.-J. Engel and R. Nagel, One Parameter Semigroups for Linear Evolution Equations, Springer Verlag, New York, 2000. |
[12] |
F. R. Gantmacher, Applications of the Theory of Matrices, Interscience Publishers, Inc. New York, 1959. |
[13] |
Ch. Godsil and G. Royle, Algebraic Graph Theory, Springer Verlag, New York, 2001.
doi: 10.1007/978-1-4613-0163-9. |
[14] |
F.M. Hante, G. Leugering and T. I. Seidman, Modeling and analysis of modal switching in networked transport systems, Appl. Math. & Optimization, 59 (2009), 275-292.
doi: 10.1007/s00245-008-9057-6. |
[15] |
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. |
[16] |
T. Matrai and E. Sikolya, Asymptotic behaviour of flows in networks, Forum Math., 19 (2007), 429-461.
doi: 10.1515/FORUM.2007.018. |
[17] |
C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, 2000.
doi: 10.1137/1.9780898719512. |
[18] |
H. Minc, Nonnegative Matrices, John Wiley & Sons, New York, 1988. |
[19] |
R. Nagel, ed., One-parameter Semigroups of Positive Operators, Springer Verlag, Berlin, 1986. |
[20] |
P. Namayanja, Transport on Network Structures, Ph.D thesis, UKZN, 2012. |
[21] |
E. Seneta, Nonnegative Matrices and Markov Chains, Springer Verlag, New York, 1981.
doi: 10.1007/0-387-32792-4. |
[22] |
E. Sikolya, Semigroups for Flows in Networks, Ph.D dissertation, University of Tübingen, 2004. |
[23] |
E. Sikolya, Flows in networks with dynamic ramification nodes, J. Evol. Equ., 5 (2005), 441-463.
doi: 10.1007/s00028-005-0221-z. |
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