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Existence and uniqueness of a solution to a three-dimensional axially symmetric Biot problem arising in modeling blood flow
1. | Department of Mathematics, University of Houston, Houston, Texas 77204-3476, United States, United States |
[1] |
Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012 |
[2] |
Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633 |
[3] |
Salim Meddahi, David Mora. Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 269-287. doi: 10.3934/dcdss.2016.9.269 |
[4] |
Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluid-structure interaction problem. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 199-220. doi: 10.3934/dcdsb.2008.9.199 |
[5] |
Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355 |
[6] |
George Avalos, Roberto Triggiani. Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 417-447. doi: 10.3934/dcdss.2009.2.417 |
[7] |
George Avalos, Thomas J. Clark. A mixed variational formulation for the wellposedness and numerical approximation of a PDE model arising in a 3-D fluid-structure interaction. Evolution Equations and Control Theory, 2014, 3 (4) : 557-578. doi: 10.3934/eect.2014.3.557 |
[8] |
Huashui Zhan. On a hyperbolic-parabolic mixed type equation. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 605-624. doi: 10.3934/dcdss.2017030 |
[9] |
Andro Mikelić, Giovanna Guidoboni, Sunčica Čanić. Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Networks and Heterogeneous Media, 2007, 2 (3) : 397-423. doi: 10.3934/nhm.2007.2.397 |
[10] |
Serge Nicaise, Cristina Pignotti. Asymptotic analysis of a simple model of fluid-structure interaction. Networks and Heterogeneous Media, 2008, 3 (4) : 787-813. doi: 10.3934/nhm.2008.3.787 |
[11] |
George Avalos, Roberto Triggiani. Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability. Evolution Equations and Control Theory, 2013, 2 (4) : 563-598. doi: 10.3934/eect.2013.2.563 |
[12] |
Daniele Boffi, Lucia Gastaldi, Sebastian Wolf. Higher-order time-stepping schemes for fluid-structure interaction problems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 3807-3830. doi: 10.3934/dcdsb.2020229 |
[13] |
George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817 |
[14] |
Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349 |
[15] |
Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295-318. doi: 10.3934/mbe.2013.10.295 |
[16] |
Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2315-2373. doi: 10.3934/dcds.2017102 |
[17] |
Henry Jacobs, Joris Vankerschaver. Fluid-structure interaction in the Lagrange-Poincaré formalism: The Navier-Stokes and inviscid regimes. Journal of Geometric Mechanics, 2014, 6 (1) : 39-66. doi: 10.3934/jgm.2014.6.39 |
[18] |
Eugenio Aulisa, Akif Ibragimov, Emine Yasemen Kaya-Cekin. Fluid structure interaction problem with changing thickness beam and slightly compressible fluid. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1133-1148. doi: 10.3934/dcdss.2014.7.1133 |
[19] |
Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424 |
[20] |
Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. FLUID STRUCTURE INTERACTION PROBLEM WITH CHANGING THICKNESS NON-LINEAR BEAM Fluid structure interaction problem with changing thickness non-linear beam. Conference Publications, 2011, 2011 (Special) : 813-823. doi: 10.3934/proc.2011.2011.813 |
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