
Previous Article
The nonlinear Schrödinger equation created by the vibrations of an elastic plate and its dimensional expansion
 PROC Home
 This Issue

Next Article
The characterization of maximal invariant sets of nonlinear discretetime control dynamical systems
Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion
1.  Department of Mathematics and Mechanics, SaintPetersburg State University, SaintPetersburg, 198504, Russian Federation, Russian Federation 
References:
[1] 
G. Duvant and J.L. Lions, "Inequalities in Mechanics and Physics,", Springer  Verlag, (1976). Google Scholar 
[2] 
D. Kalinichenko, V. Reitmann and S. Skopinov, Stability and bifurcations in a finite time interval on variational inequalities,, Differential Equations, 48 (2012), 1. Google Scholar 
[3] 
Y. Kalinin, V. Reitmann and N. Yumaguzin, Asymptotic behavior of Maxwell's equation in onespace dimension with thermal effect,, Discrete and Continuous Dynamical Systems  Supplement 2011, 2 (2011), 754. Google Scholar 
[4] 
A.L. Likhtarnikov and V.A. Yakubovich, The frequency theorem for equations of evolutionary type,, Siberian Math. J., 17 (1976), 790. Google Scholar 
[5] 
R.V. Manoranjan, H.M. Yin and R. Showalter, On twophase Stefan problem arising from a microwave heating process,, Contin. and Discrete Dynamical Systems, 15 (2006), 1155. Google Scholar 
[6] 
A.N. Michel and D.W. Porter, Practical stability and finitetime stability of discontinuous systems,, IEEE Trans. Circuit Theory, 19 (1972), 123. Google Scholar 
[7] 
A.A. Pankov, "Bounded and Almost Periodic Solutions of Nonlinear Differential Operator Equations,", Naukova Dumka, (1986). Google Scholar 
[8] 
H. Triebel, "Interpolation Theorie, Function Spaces, Differential Operators,", Amsterdam, (1978). Google Scholar 
[9] 
L. Weiss and E.F. Infante, On the stability of systems defined over a finite time interval,, Proc. Nat. Acad. Sci., 54 (1965), 44. Google Scholar 
show all references
References:
[1] 
G. Duvant and J.L. Lions, "Inequalities in Mechanics and Physics,", Springer  Verlag, (1976). Google Scholar 
[2] 
D. Kalinichenko, V. Reitmann and S. Skopinov, Stability and bifurcations in a finite time interval on variational inequalities,, Differential Equations, 48 (2012), 1. Google Scholar 
[3] 
Y. Kalinin, V. Reitmann and N. Yumaguzin, Asymptotic behavior of Maxwell's equation in onespace dimension with thermal effect,, Discrete and Continuous Dynamical Systems  Supplement 2011, 2 (2011), 754. Google Scholar 
[4] 
A.L. Likhtarnikov and V.A. Yakubovich, The frequency theorem for equations of evolutionary type,, Siberian Math. J., 17 (1976), 790. Google Scholar 
[5] 
R.V. Manoranjan, H.M. Yin and R. Showalter, On twophase Stefan problem arising from a microwave heating process,, Contin. and Discrete Dynamical Systems, 15 (2006), 1155. Google Scholar 
[6] 
A.N. Michel and D.W. Porter, Practical stability and finitetime stability of discontinuous systems,, IEEE Trans. Circuit Theory, 19 (1972), 123. Google Scholar 
[7] 
A.A. Pankov, "Bounded and Almost Periodic Solutions of Nonlinear Differential Operator Equations,", Naukova Dumka, (1986). Google Scholar 
[8] 
H. Triebel, "Interpolation Theorie, Function Spaces, Differential Operators,", Amsterdam, (1978). Google Scholar 
[9] 
L. Weiss and E.F. Infante, On the stability of systems defined over a finite time interval,, Proc. Nat. Acad. Sci., 54 (1965), 44. Google Scholar 
[1] 
Yuri Kalinin, Volker Reitmann, Nayil Yumaguzin. Asymptotic behavior of Maxwell's equation in onespace dimension with thermal effect. Conference Publications, 2011, 2011 (Special) : 754762. doi: 10.3934/proc.2011.2011.754 
[2] 
Hongwei Zhang, Qingying Hu. Asymptotic behavior and nonexistence of wave equation with nonlinear boundary condition. Communications on Pure & Applied Analysis, 2005, 4 (4) : 861869. doi: 10.3934/cpaa.2005.4.861 
[3] 
T. A. Shaposhnikova, M. N. Zubova. Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks & Heterogeneous Media, 2008, 3 (3) : 675689. doi: 10.3934/nhm.2008.3.675 
[4] 
S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155165. doi: 10.3934/jimo.2008.4.155 
[5] 
M. Ben Ayed, Abdelbaki Selmi. Asymptotic behavior and existence results for a biharmonic equation involving the critical Sobolev exponent in a fivedimensional domain. Communications on Pure & Applied Analysis, 2010, 9 (6) : 17051722. doi: 10.3934/cpaa.2010.9.1705 
[6] 
Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 11171137. doi: 10.3934/ipi.2014.8.1117 
[7] 
Gang Bao, Bin Hu, Peijun Li, Jue Wang. Analysis of timedomain Maxwell's equations in biperiodic structures. Discrete & Continuous Dynamical Systems  B, 2020, 25 (1) : 259286. doi: 10.3934/dcdsb.2019181 
[8] 
Haiyang He. Asymptotic behavior of the ground state Solutions for Hénon equation with Robin boundary condition. Communications on Pure & Applied Analysis, 2013, 12 (6) : 23932408. doi: 10.3934/cpaa.2013.12.2393 
[9] 
M. Eller. On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition. Discrete & Continuous Dynamical Systems  S, 2009, 2 (3) : 473481. doi: 10.3934/dcdss.2009.2.473 
[10] 
Bernard Brighi, S. Guesmia. Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain. Conference Publications, 2007, 2007 (Special) : 160169. doi: 10.3934/proc.2007.2007.160 
[11] 
Shijin Deng, Linglong Du, ShihHsien Yu. Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition. Kinetic & Related Models, 2013, 6 (4) : 865882. doi: 10.3934/krm.2013.6.865 
[12] 
Michel Chipot, Karen Yeressian. On the asymptotic behavior of variational inequalities set in cylinders. Discrete & Continuous Dynamical Systems  A, 2013, 33 (11&12) : 48754890. doi: 10.3934/dcds.2013.33.4875 
[13] 
Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete & Continuous Dynamical Systems  A, 2009, 25 (2) : 545565. doi: 10.3934/dcds.2009.25.545 
[14] 
Khalid Latrach, Hatem Megdiche. Time asymptotic behaviour for Rotenberg's model with Maxwell boundary conditions. Discrete & Continuous Dynamical Systems  A, 2011, 29 (1) : 305321. doi: 10.3934/dcds.2011.29.305 
[15] 
Ivonne Rivas, Muhammad Usman, BingYu Zhang. Global wellposedness and asymptotic behavior of a class of initialboundaryvalue problem of the KortewegDe Vries equation on a finite domain. Mathematical Control & Related Fields, 2011, 1 (1) : 6181. doi: 10.3934/mcrf.2011.1.61 
[16] 
Xiaofei Cao, Guowei Dai. Stability analysis of a model on varying domain with the Robin boundary condition. Discrete & Continuous Dynamical Systems  S, 2017, 10 (5) : 935942. doi: 10.3934/dcdss.2017048 
[17] 
Ming Mei, Bruno Rubino, Rosella Sampalmieri. Asymptotic behavior of solutions to the bipolar hydrodynamic model of semiconductors in bounded domain. Kinetic & Related Models, 2012, 5 (3) : 537550. doi: 10.3934/krm.2012.5.537 
[18] 
Everaldo S. de Medeiros, Jianfu Yang. Asymptotic behavior of solutions to a perturbed pLaplacian problem with Neumann condition. Discrete & Continuous Dynamical Systems  A, 2005, 12 (4) : 595606. doi: 10.3934/dcds.2005.12.595 
[19] 
S. S. Krigman. Exact boundary controllability of Maxwell's equations with weak conductivity in the heterogeneous medium inside a general domain. Conference Publications, 2007, 2007 (Special) : 590601. doi: 10.3934/proc.2007.2007.590 
[20] 
Hakima Bessaih, Yalchin Efendiev, Florin Maris. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition. Networks & Heterogeneous Media, 2015, 10 (2) : 343367. doi: 10.3934/nhm.2015.10.343 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]