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Fluidstructure interaction in a prestressed tube with thick elastic walls I: the stationary Stokes problem
1.  Université de Lyon, Lyon, F69003, Université Lyon 1, Institut Camille Jordan, UFR Mathématiques, Site de Gerland, Bat. A, 50, avenue Tony Garnier, 69367 Lyon Cedex 07, France 
2.  Department of Mathematics, University of Houston, Houston, Texas 772043476, United States 
3.  Department of Mathematics, University of Houston, Houston, TX 772043476, United States 
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Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluidstructure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179193. doi: 10.3934/mbe.2017012 
[2] 
Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluidstructure interaction problem. Discrete & Continuous Dynamical Systems  A, 2003, 9 (3) : 633650. doi: 10.3934/dcds.2003.9.633 
[3] 
Taebeom Kim, Sunčica Čanić, Giovanna Guidoboni. Existence and uniqueness of a solution to a threedimensional axially symmetric Biot problem arising in modeling blood flow. Communications on Pure & Applied Analysis, 2010, 9 (4) : 839865. doi: 10.3934/cpaa.2010.9.839 
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Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluidstructure interaction problem. Discrete & Continuous Dynamical Systems  B, 2008, 9 (2) : 199220. doi: 10.3934/dcdsb.2008.9.199 
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Serge Nicaise, Cristina Pignotti. Asymptotic analysis of a simple model of fluidstructure interaction. Networks & Heterogeneous Media, 2008, 3 (4) : 787813. doi: 10.3934/nhm.2008.3.787 
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Igor Kukavica, Amjad Tuffaha. Solutions to a fluidstructure interaction free boundary problem. Discrete & Continuous Dynamical Systems  A, 2012, 32 (4) : 13551389. doi: 10.3934/dcds.2012.32.1355 
[7] 
Leo Howden, Donald Giddings, Henry Power, Michael Vloeberghs. Threedimensional cerebrospinal fluid flow within the human central nervous system. Discrete & Continuous Dynamical Systems  B, 2011, 15 (4) : 957969. doi: 10.3934/dcdsb.2011.15.957 
[8] 
George Avalos, Roberto Triggiani. Fluidstructure interaction with and without internal dissipation of the structure: A contrast study in stability. Evolution Equations & Control Theory, 2013, 2 (4) : 563598. doi: 10.3934/eect.2013.2.563 
[9] 
George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluidstructure interaction with boundary dissipation at the interface. Discrete & Continuous Dynamical Systems  A, 2008, 22 (4) : 817833. doi: 10.3934/dcds.2008.22.817 
[10] 
Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary  lattice Boltzmann method for fluidstructure interaction. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020349 
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Salim Meddahi, David Mora. Nonconforming mixed finite element approximation of a fluidstructure interaction spectral problem. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 269287. doi: 10.3934/dcdss.2016.9.269 
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Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluidstructure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295318. doi: 10.3934/mbe.2013.10.295 
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Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluidstructure interaction systems. Discrete & Continuous Dynamical Systems  A, 2017, 37 (5) : 23152373. doi: 10.3934/dcds.2017102 
[14] 
George Avalos, Thomas J. Clark. A mixed variational formulation for the wellposedness and numerical approximation of a PDE model arising in a 3D fluidstructure interaction. Evolution Equations & Control Theory, 2014, 3 (4) : 557578. doi: 10.3934/eect.2014.3.557 
[15] 
Henry Jacobs, Joris Vankerschaver. Fluidstructure interaction in the LagrangePoincaré formalism: The NavierStokes and inviscid regimes. Journal of Geometric Mechanics, 2014, 6 (1) : 3966. doi: 10.3934/jgm.2014.6.39 
[16] 
Daniele Boffi, Lucia Gastaldi, Sebastian Wolf. Higherorder timestepping schemes for fluidstructure interaction problems. Discrete & Continuous Dynamical Systems  B, 2020, 25 (10) : 38073830. doi: 10.3934/dcdsb.2020229 
[17] 
Hao Chen, Kaitai Li, Yuchuan Chu, Zhiqiang Chen, Yiren Yang. A dimension splitting and characteristic projection method for threedimensional incompressible flow. Discrete & Continuous Dynamical Systems  B, 2019, 24 (1) : 127147. doi: 10.3934/dcdsb.2018111 
[18] 
George Avalos, Roberto Triggiani. Semigroup wellposedness in the energy space of a parabolichyperbolic coupled StokesLamé PDE system of fluidstructure interaction. Discrete & Continuous Dynamical Systems  S, 2009, 2 (3) : 417447. doi: 10.3934/dcdss.2009.2.417 
[19] 
Baoquan Yuan, Xiao Li. Blowup criteria of smooth solutions to the threedimensional micropolar fluid equations in Besov space. Discrete & Continuous Dynamical Systems  S, 2016, 9 (6) : 21672179. doi: 10.3934/dcdss.2016090 
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ChengJie Liu, YaGuang Wang, Tong Yang. Global existence of weak solutions to the threedimensional Prandtl equations with a special structure. Discrete & Continuous Dynamical Systems  S, 2016, 9 (6) : 20112029. doi: 10.3934/dcdss.2016082 
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