-
Previous Article
Gaussian estimates on networks with applications to optimal control
- NHM Home
- This Issue
-
Next Article
Perturbation and numerical methods for computing the minimal average energy
Spectral theory for nonconservative transmission line networks
1. | Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80933, United States |
References:
[1] |
A. Agarwal, S. Das and D. Sen, Power dissipation for systems with junctions of multiple quantum wires, Physical Review B, 81 (2010). |
[2] |
L. Ahlfors, "Complex Analysis," McGraw-Hill, New York, 1966. |
[3] |
F. Ali Mehmeti, "Nonlinear Waves in Networks," Akademie Verlag, Berlin, 1994. |
[4] |
R. Carlson, Inverse eigenvalue problems on directed graphs, Transactions of the American Mathematical Society, 351 (1999), 4069-4088.
doi: 10.1090/S0002-9947-99-02175-3. |
[5] |
R. Carlson, Linear network models related to blood flow, in Quantum Graphs and Their Applications, Contemporary Mathematics, 415 (2006), 65-80. |
[6] |
C. Cattaneo and L. Fontana, D'Alembert formula on finite one-dimensional networks, J. Math. Anal. Appl., 284 (2003), 403-424.
doi: 10.1016/S0022-247X(02)00392-X. |
[7] |
G. Chen, S. Krantz, D. Russell, C. Wayne, H. West and M. Coleman, Analysis, designs, and behavior of dissipative joints for coupled beams, SIAM Journal on Applied Mathematics., 49 (1989), 1665-1693.
doi: 10.1137/0149101. |
[8] |
S. Cox and E. Zuazua, The rate at which energy decays in a string damped at one end, Indiana Univ. Math. J., 44 (1995), 545-573.
doi: 10.1512/iumj.1995.44.2001. |
[9] |
E. B. Davies, Eigenvalues of an elliptic system, Math. Z., 243 (2003), 719-743.
doi: 10.1007/s00209-002-0464-0. |
[10] |
E. B. Davies, P. Exner and J. Lipovsky, Non-Weyl asymptotics for quantum graphs with general coupling conditions, J. Phys. A, 43 (2010). |
[11] | |
[12] |
I. Herstein, "Topics in Algebra," Xerox College Publishing, Waltham, 1964. |
[13] |
B. Jessen and H. Tornhave, Mean motions and zeros of almost periodic functions, Acta Math., 77 (1945), 137-279.
doi: 10.1007/BF02392225. |
[14] |
T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, New York, 1995. |
[15] |
V. Kostrykin, J. Potthoff and R. Schrader, Contraction semigroups on metric graphs, in Analysis on Graphs and Its Applications, PSUM, 77 (2008), 423-458. |
[16] |
T. Kottos and U. Smilansky, Periodic orbit theory and spectral statistics for quantum graphs, Ann. Phys., 274 (1999), 76-124.
doi: 10.1006/aphy.1999.5904. |
[17] |
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. |
[18] |
M. Kramar Fijavz, D. Mugnolo and E. Sikolya, Variational and semigroup methods for waves and diffusions in networks, Appl. Math. Optim., 55 (2007), 219-240.
doi: 10.1007/s00245-006-0887-9. |
[19] |
M. Krein and A. Nudelman, Some spectral properties of a nonhomogeneous string with a dissipative boundary condition, J. Operator Theory, 22 (1989), 369-395. |
[20] |
B. Levin, "Distribution of Zeros of Entire Functions," American Mathematical Society, Providence, 1980. |
[21] | |
[22] |
G. Lumer, "Equations de Diffusion Generales sur des Reseaux Infinis," Seminar Goulaouic-Schwartz, 1980. |
[23] |
G. Lumer, "Connecting of Local Operators and Evolution Equations on Networks," Lecture Notes in Math., 787, Springer, 1980. |
[24] |
P. Magnusson, G. Alexander, V. Tripathi and A. Weisshaar, "Transmission Lines and Wave Propagation," CRC Press, Boca Raton, 2001. |
[25] |
G. Miano and A. Maffucci, "Transmission Lines and Lumped Circuits," Academic Press, San Diego, 2001. |
[26] |
L. J. Myers and W. L. Capper, A transmission line model of the human foetal circulatory system, Medical Engineering and Physics, 24 (2002), 285-294.
doi: 10.1016/S1350-4533(02)00019-X. |
[27] |
S. Nicaise, Spectre des reseaux topologiques finis, Bulletin des sciences mathematique, 111 (1987), 401-413. |
[28] |
J. Ottesen, M. Olufsen and J. Larsen, "Applied Mathematical Models in Human Physiology," SIAM, 2004.
doi: 10.1137/1.9780898718287. |
[29] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer, New York, 1983. |
[30] |
S. Sherwin, V. Franke, J. Peiro and K. Parker, One-dimensional modeling of a vascular network in space-time variables, Journal of Engineering Mathematics, 47 (2003), 217-250.
doi: 10.1023/B:ENGI.0000007979.32871.e2. |
[31] |
J. von Below, A characteristic equation associated to an eigenvalue problem on C2 networks, Lin. Alg. Appl., 71 (1985), 309-325.
doi: 10.1016/0024-3795(85)90258-7. |
[32] |
L. Zhou and G. Kriegsmann, A simple derivation of microstrip transmission line equations, SIAM J. Appl. Math., 70 (2009), 353-367.
doi: 10.1137/080737563. |
show all references
References:
[1] |
A. Agarwal, S. Das and D. Sen, Power dissipation for systems with junctions of multiple quantum wires, Physical Review B, 81 (2010). |
[2] |
L. Ahlfors, "Complex Analysis," McGraw-Hill, New York, 1966. |
[3] |
F. Ali Mehmeti, "Nonlinear Waves in Networks," Akademie Verlag, Berlin, 1994. |
[4] |
R. Carlson, Inverse eigenvalue problems on directed graphs, Transactions of the American Mathematical Society, 351 (1999), 4069-4088.
doi: 10.1090/S0002-9947-99-02175-3. |
[5] |
R. Carlson, Linear network models related to blood flow, in Quantum Graphs and Their Applications, Contemporary Mathematics, 415 (2006), 65-80. |
[6] |
C. Cattaneo and L. Fontana, D'Alembert formula on finite one-dimensional networks, J. Math. Anal. Appl., 284 (2003), 403-424.
doi: 10.1016/S0022-247X(02)00392-X. |
[7] |
G. Chen, S. Krantz, D. Russell, C. Wayne, H. West and M. Coleman, Analysis, designs, and behavior of dissipative joints for coupled beams, SIAM Journal on Applied Mathematics., 49 (1989), 1665-1693.
doi: 10.1137/0149101. |
[8] |
S. Cox and E. Zuazua, The rate at which energy decays in a string damped at one end, Indiana Univ. Math. J., 44 (1995), 545-573.
doi: 10.1512/iumj.1995.44.2001. |
[9] |
E. B. Davies, Eigenvalues of an elliptic system, Math. Z., 243 (2003), 719-743.
doi: 10.1007/s00209-002-0464-0. |
[10] |
E. B. Davies, P. Exner and J. Lipovsky, Non-Weyl asymptotics for quantum graphs with general coupling conditions, J. Phys. A, 43 (2010). |
[11] | |
[12] |
I. Herstein, "Topics in Algebra," Xerox College Publishing, Waltham, 1964. |
[13] |
B. Jessen and H. Tornhave, Mean motions and zeros of almost periodic functions, Acta Math., 77 (1945), 137-279.
doi: 10.1007/BF02392225. |
[14] |
T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, New York, 1995. |
[15] |
V. Kostrykin, J. Potthoff and R. Schrader, Contraction semigroups on metric graphs, in Analysis on Graphs and Its Applications, PSUM, 77 (2008), 423-458. |
[16] |
T. Kottos and U. Smilansky, Periodic orbit theory and spectral statistics for quantum graphs, Ann. Phys., 274 (1999), 76-124.
doi: 10.1006/aphy.1999.5904. |
[17] |
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. |
[18] |
M. Kramar Fijavz, D. Mugnolo and E. Sikolya, Variational and semigroup methods for waves and diffusions in networks, Appl. Math. Optim., 55 (2007), 219-240.
doi: 10.1007/s00245-006-0887-9. |
[19] |
M. Krein and A. Nudelman, Some spectral properties of a nonhomogeneous string with a dissipative boundary condition, J. Operator Theory, 22 (1989), 369-395. |
[20] |
B. Levin, "Distribution of Zeros of Entire Functions," American Mathematical Society, Providence, 1980. |
[21] | |
[22] |
G. Lumer, "Equations de Diffusion Generales sur des Reseaux Infinis," Seminar Goulaouic-Schwartz, 1980. |
[23] |
G. Lumer, "Connecting of Local Operators and Evolution Equations on Networks," Lecture Notes in Math., 787, Springer, 1980. |
[24] |
P. Magnusson, G. Alexander, V. Tripathi and A. Weisshaar, "Transmission Lines and Wave Propagation," CRC Press, Boca Raton, 2001. |
[25] |
G. Miano and A. Maffucci, "Transmission Lines and Lumped Circuits," Academic Press, San Diego, 2001. |
[26] |
L. J. Myers and W. L. Capper, A transmission line model of the human foetal circulatory system, Medical Engineering and Physics, 24 (2002), 285-294.
doi: 10.1016/S1350-4533(02)00019-X. |
[27] |
S. Nicaise, Spectre des reseaux topologiques finis, Bulletin des sciences mathematique, 111 (1987), 401-413. |
[28] |
J. Ottesen, M. Olufsen and J. Larsen, "Applied Mathematical Models in Human Physiology," SIAM, 2004.
doi: 10.1137/1.9780898718287. |
[29] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer, New York, 1983. |
[30] |
S. Sherwin, V. Franke, J. Peiro and K. Parker, One-dimensional modeling of a vascular network in space-time variables, Journal of Engineering Mathematics, 47 (2003), 217-250.
doi: 10.1023/B:ENGI.0000007979.32871.e2. |
[31] |
J. von Below, A characteristic equation associated to an eigenvalue problem on C2 networks, Lin. Alg. Appl., 71 (1985), 309-325.
doi: 10.1016/0024-3795(85)90258-7. |
[32] |
L. Zhou and G. Kriegsmann, A simple derivation of microstrip transmission line equations, SIAM J. Appl. Math., 70 (2009), 353-367.
doi: 10.1137/080737563. |
[1] |
Barbara Bianconi, Francesca Papalini. Non-autonomous boundary value problems on the real line. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 759-776. doi: 10.3934/dcds.2006.15.759 |
[2] |
Stefano Biagi, Teresa Isernia. On the solvability of singular boundary value problems on the real line in the critical growth case. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 1131-1157. doi: 10.3934/dcds.2020073 |
[3] |
Long Hu, Tatsien Li, Bopeng Rao. Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type. Communications on Pure and Applied Analysis, 2014, 13 (2) : 881-901. doi: 10.3934/cpaa.2014.13.881 |
[4] |
Sergei Avdonin, Pavel Kurasov, Marlena Nowaczyk. Inverse problems for quantum trees II: Recovering matching conditions for star graphs. Inverse Problems and Imaging, 2010, 4 (4) : 579-598. doi: 10.3934/ipi.2010.4.579 |
[5] |
Vesselin Petkov. Location of eigenvalues for the wave equation with dissipative boundary conditions. Inverse Problems and Imaging, 2016, 10 (4) : 1111-1139. doi: 10.3934/ipi.2016034 |
[6] |
C. Bourdarias, M. Gisclon, A. Omrane. Transmission boundary conditions in a model-kinetic decomposition. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 69-94. doi: 10.3934/dcdsb.2002.2.69 |
[7] |
Bruno Fornet, O. Guès. Penalization approach to semi-linear symmetric hyperbolic problems with dissipative boundary conditions. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 827-845. doi: 10.3934/dcds.2009.23.827 |
[8] |
Colin J. Cotter, Darryl D. Holm. Geodesic boundary value problems with symmetry. Journal of Geometric Mechanics, 2010, 2 (1) : 51-68. doi: 10.3934/jgm.2010.2.51 |
[9] |
Hiroshi Watanabe. Solvability of boundary value problems for strongly degenerate parabolic equations with discontinuous coefficients. Discrete and Continuous Dynamical Systems - S, 2014, 7 (1) : 177-189. doi: 10.3934/dcdss.2014.7.177 |
[10] |
Iñigo U. Erneta. Well-posedness for boundary value problems for coagulation-fragmentation equations. Kinetic and Related Models, 2020, 13 (4) : 815-835. doi: 10.3934/krm.2020028 |
[11] |
Oleksandr Boichuk, Victor Feruk. Boundary-value problems for weakly singular integral equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1379-1395. doi: 10.3934/dcdsb.2021094 |
[12] |
Hung Le. Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3357-3385. doi: 10.3934/dcds.2018144 |
[13] |
Youngmok Jeon, Dongwook Shin. Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions. Electronic Research Archive, 2021, 29 (5) : 3361-3382. doi: 10.3934/era.2021043 |
[14] |
Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3063-3092. doi: 10.3934/dcds.2020398 |
[15] |
Laurence Halpern, Jeffrey Rauch. Hyperbolic boundary value problems with trihedral corners. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4403-4450. doi: 10.3934/dcds.2016.36.4403 |
[16] |
Felix Sadyrbaev. Nonlinear boundary value problems of the calculus of variations. Conference Publications, 2003, 2003 (Special) : 760-770. doi: 10.3934/proc.2003.2003.760 |
[17] |
J. R. L. Webb. Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 177-186. doi: 10.3934/dcdss.2008.1.177 |
[18] |
Sergei Avdonin, Fritz Gesztesy, Konstantin A. Makarov. Spectral estimation and inverse initial boundary value problems. Inverse Problems and Imaging, 2010, 4 (1) : 1-9. doi: 10.3934/ipi.2010.4.1 |
[19] |
G. Infante. Positive solutions of nonlocal boundary value problems with singularities. Conference Publications, 2009, 2009 (Special) : 377-384. doi: 10.3934/proc.2009.2009.377 |
[20] |
John R. Graef, Lingju Kong, Qingkai Kong, Min Wang. Positive solutions of nonlocal fractional boundary value problems. Conference Publications, 2013, 2013 (special) : 283-290. doi: 10.3934/proc.2013.2013.283 |
2020 Impact Factor: 1.213
Tools
Metrics
Other articles
by authors
[Back to Top]