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Schrödinger equations with nonlinearity of integral type
Homogenization of timedependent systems with KelvinVoigt damping by twoscale convergence
1.  Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, United States 
[1] 
Louis Tebou. Stabilization of some elastodynamic systems with localized KelvinVoigt damping. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 71177136. doi: 10.3934/dcds.2016110 
[2] 
Fathi Hassine. Asymptotic behavior of the transmission EulerBernoulli plate and wave equation with a localized KelvinVoigt damping. Discrete & Continuous Dynamical Systems  B, 2016, 21 (6) : 17571774. doi: 10.3934/dcdsb.2016021 
[3] 
Serge Nicaise, Cristina Pignotti. Stability of the wave equation with localized KelvinVoigt damping and boundary delay feedback. Discrete & Continuous Dynamical Systems  S, 2016, 9 (3) : 791813. doi: 10.3934/dcdss.2016029 
[4] 
Erik Kropat, Silja MeyerNieberg, GerhardWilhelm Weber. Bridging the gap between variational homogenization results and twoscale asymptotic averaging techniques on periodic network structures. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 223250. doi: 10.3934/naco.2017016 
[5] 
Miroslav Bulíček, Josef Málek, K. R. Rajagopal. On KelvinVoigt model and its generalizations. Evolution Equations & Control Theory, 2012, 1 (1) : 1742. doi: 10.3934/eect.2012.1.17 
[6] 
Ali Wehbe, Rayan Nasser, Nahla Noun. Stability of ND transmission problem in viscoelasticity with localized KelvinVoigt damping under different types of geometric conditions. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020050 
[7] 
Aurore Back, Emmanuel Frénod. Geometric twoscale convergence on manifold and applications to the Vlasov equation. Discrete & Continuous Dynamical Systems  S, 2015, 8 (1) : 223241. doi: 10.3934/dcdss.2015.8.223 
[8] 
Alexander Mielke, Sina Reichelt, Marita Thomas. Twoscale homogenization of nonlinear reactiondiffusion systems with slow diffusion. Networks & Heterogeneous Media, 2014, 9 (2) : 353382. doi: 10.3934/nhm.2014.9.353 
[9] 
Xiaobin Yao, Qiaozhen Ma, Tingting Liu. Asymptotic behavior for stochastic plate equations with rotational inertia and KelvinVoigt dissipative term on unbounded domains. Discrete & Continuous Dynamical Systems  B, 2019, 24 (4) : 18891917. doi: 10.3934/dcdsb.2018247 
[10] 
Manil T. Mohan. Global attractors, exponential attractors and determining modes for the three dimensional KelvinVoigt fluids with "fading memory". Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020105 
[11] 
Manil T. Mohan. On the three dimensional KelvinVoigt fluids: global solvability, exponential stability and exact controllability of Galerkin approximations. Evolution Equations & Control Theory, 2020, 9 (2) : 301339. doi: 10.3934/eect.2020007 
[12] 
Alexandre Mouton. Twoscale semiLagrangian simulation of a charged particle beam in a periodic focusing channel. Kinetic & Related Models, 2009, 2 (2) : 251274. doi: 10.3934/krm.2009.2.251 
[13] 
Zhiqiang Yang, Junzhi Cui, Qiang Ma. The secondorder twoscale computation for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials. Discrete & Continuous Dynamical Systems  B, 2014, 19 (3) : 827848. doi: 10.3934/dcdsb.2014.19.827 
[14] 
Fang Liu, Aihui Zhou. Localizations and parallelizations for twoscale finite element discretizations. Communications on Pure & Applied Analysis, 2007, 6 (3) : 757773. doi: 10.3934/cpaa.2007.6.757 
[15] 
Alexandre Mouton. Expansion of a singularly perturbed equation with a twoscale converging convection term. Discrete & Continuous Dynamical Systems  S, 2016, 9 (5) : 14471473. doi: 10.3934/dcdss.2016058 
[16] 
Ibrahima Faye, Emmanuel Frénod, Diaraf Seck. TwoScale numerical simulation of sand transport problems. Discrete & Continuous Dynamical Systems  S, 2015, 8 (1) : 151168. doi: 10.3934/dcdss.2015.8.151 
[17] 
Jingwei Hu, Shi Jin, Li Wang. An asymptoticpreserving scheme for the semiconductor Boltzmann equation with twoscale collisions: A splitting approach. Kinetic & Related Models, 2015, 8 (4) : 707723. doi: 10.3934/krm.2015.8.707 
[18] 
Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a twoscale linear transport equation. Networks & Heterogeneous Media, 2006, 1 (1) : 143166. doi: 10.3934/nhm.2006.1.143 
[19] 
Shi Jin, Xu Yang, Guangwei Yuan. A domain decomposition method for a twoscale transport equation with energy flux conserved at the interface. Kinetic & Related Models, 2008, 1 (1) : 6584. doi: 10.3934/krm.2008.1.65 
[20] 
Andriy Bondarenko, Guy Bouchitté, Luísa Mascarenhas, Rajesh Mahadevan. Rate of convergence for correctors in almost periodic homogenization. Discrete & Continuous Dynamical Systems, 2005, 13 (2) : 503514. doi: 10.3934/dcds.2005.13.503 
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