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A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part I: Formulation, Analysis, and Computations
A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part II: Analysis of Convergence
1. | Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig |
2. | Department of Computer Science, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, United States |
3. | Department of Mathematics, University of Maryland, College Park, MD 20742, United States |
[1] |
Stuart S. Antman, David Bourne. A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part I: Formulation, Analysis, and Computations. Communications on Pure and Applied Analysis, 2009, 8 (1) : 123-142. doi: 10.3934/cpaa.2009.8.123 |
[2] |
Johannes Elschner, George C. Hsiao, Andreas Rathsfeld. An inverse problem for fluid-solid interaction. Inverse Problems and Imaging, 2008, 2 (1) : 83-120. doi: 10.3934/ipi.2008.2.83 |
[3] |
Andreas Kirsch, Albert Ruiz. The Factorization Method for an inverse fluid-solid interaction scattering problem. Inverse Problems and Imaging, 2012, 6 (4) : 681-695. doi: 10.3934/ipi.2012.6.681 |
[4] |
Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations and Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83 |
[5] |
Francesca Bucci, Irena Lasiecka. Regularity of boundary traces for a fluid-solid interaction model. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 505-521. doi: 10.3934/dcdss.2011.4.505 |
[6] |
Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations and Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59 |
[7] |
Peter Monk, Virginia Selgas. An inverse fluid--solid interaction problem. Inverse Problems and Imaging, 2009, 3 (2) : 173-198. doi: 10.3934/ipi.2009.3.173 |
[8] |
Wen Deng. Resolvent estimates for a two-dimensional non-self-adjoint operator. Communications on Pure and Applied Analysis, 2013, 12 (1) : 547-596. doi: 10.3934/cpaa.2013.12.547 |
[9] |
Peter Monk, Virginia Selgas. Near field sampling type methods for the inverse fluid--solid interaction problem. Inverse Problems and Imaging, 2011, 5 (2) : 465-483. doi: 10.3934/ipi.2011.5.465 |
[10] |
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 |
[11] |
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 |
[12] |
O. A. Veliev. On the spectrality and spectral expansion of the non-self-adjoint mathieu-hill operator in $ L_{2}(-\infty, \infty) $. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1537-1562. doi: 10.3934/cpaa.2020077 |
[13] |
Mourad Bellassoued, Ibtissem Ben Aïcha, Zouhour Rezig. Stable determination of a vector field in a non-Self-Adjoint dynamical Schrödinger equation on Riemannian manifolds. Mathematical Control and Related Fields, 2021, 11 (2) : 403-431. doi: 10.3934/mcrf.2020042 |
[14] |
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 |
[15] |
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 |
[16] |
Tamara Fastovska. Long-time behaviour of a radially symmetric fluid-shell interaction system. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1315-1348. doi: 10.3934/dcds.2018054 |
[17] |
Lorena Bociu, Jean-Paul Zolésio. Existence for the linearization of a steady state fluid/nonlinear elasticity interaction. Conference Publications, 2011, 2011 (Special) : 184-197. doi: 10.3934/proc.2011.2011.184 |
[18] |
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 |
[19] |
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 |
[20] |
Muhammad Bilal Riaz, Naseer Ahmad Asif, Abdon Atangana, Muhammad Imran Asjad. Couette flows of a viscous fluid with slip effects and non-integer order derivative without singular kernel. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 645-664. doi: 10.3934/dcdss.2019041 |
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