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Preface
Fluid structure interaction problem with changing thickness beam and slightly compressible fluid
1. | Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042 |
2. | Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States |
References:
[1] |
E. Aulisa, L. Bloshanskaya and A. Ibragimov, Long-term dynamics for well productivity index for nonlinear flows in porous media, Journal of Mathematical Physics, 52 (2011), 023506, 26 pp.
doi: 10.1063/1.3536463. |
[2] |
E. Aulisa, A. Cervone, S. Manservisi and P. Seshaiyer, A multilevel domain decomposition approach for studying coupled flow application, Communications in Computational Physics, 6 (2009), 319-341.
doi: 10.4208/cicp.2009.v6.p319. |
[3] |
M. Boulakia and S. Guerrero, A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations, Ann. Inst. H. Poincare Anal. Non Lineaire, 26 (2009), 777-813.
doi: 10.1016/j.anihpc.2008.02.004. |
[4] |
I. D. Chueshov, A global attractor for a fluid-plate interaction model accounting only for longitudinal deformations of the plate, Mathematical Methods in the Applied Sciences, 34 (2011), 1801-1812.
doi: doi:10.1002/mma.1496. |
[5] |
D. Coutand and S. Shkoller, Motion of an elastic solid inside an incompressible viscous fluid, Arch. Ration. Mech. Anal., 176 (2005), 25-102.
doi: 10.1007/s00205-004-0340-7. |
[6] |
Q. Du, M. D. Gunzburger, L. S. Hou and J. Lee, Analysis of a linear fluid-structure interaction problem, Discrete and Continuous Dynamical Systems, 9 (2003), 633-650.
doi: 10.3934/dcds.2003.9.633. |
[7] |
F. Flori and P. Orenga, Fluid-structure interaction: Analysis of a 3-D compressible model, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 17 (2000), 753-777.
doi: 10.1016/S0294-1449(00)00119-0. |
[8] |
D. G. Gorman, I. Trendafilova, A. J. Mulholland and J. Horacek, Analytical modeling and extraction of the modal behavior of a cantilever beam in fluid interaction, Journal of Sound and Vibration, 308 (2007), 231-245.
doi: 10.1016/j.jsv.2007.07.032. |
[9] |
C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, SIAM Journal on Mathematical Analysis, 40 (2008), 716-737.
doi: 10.1137/070699196. |
[10] |
M. Grobbelaar Van Dalsen, On a fluid-structure model in which the dynamics of the structure involves the shear stress due to the fluid, Journal of Mathematical Fluid Mechanics, 10 (2008), 388-401.
doi: 10.1007/s00021-006-0236-4. |
[11] |
M. Grobbelaar Van Dalsen, Strong stability for a fluid structure interaction model, Math. Meth. Appl. Sci., 32 (2009), 1452-1466.
doi: 10.1002/mma.1104. |
[12] |
J. Hron and S. Turek, A Monolithic FEM/ Multigrid solver for ALE formulation of fluid structure interaction with applications in biomechanics, Lecture Notes in Computational Science and Engineering, 53 (2006), 146-170.
doi: 10.1007/3-540-34596-5_7. |
[13] |
E. Kaya-Cekin, E. Aulisa and A. Ibragimov, Fluid structure interaction problem with changing thickness non-linear beam, Discrete And Continuous Dynamical Systems, Supplement, II (2011), 813-823. |
[14] |
E. Kaya-Cekin, E. Aulisa and A. Ibragimov, Stability Analysis of non-linear plates coupled with Darcy flows, Evolution Equation and Control Theory, 2 (2013), 193-232.
doi: 10.3934/eect.2013.2.193. |
[15] |
E. Kaya-Cekin, E. Aulisa, A. Ibragimov and P. Seshaiyer, A Stability Estimate for Fluid Structure Interaction Problem with Non-Linear Beam, Discrete And Continuous Dynamical Systems. Supplement, (2009), 424-432. |
[16] |
E. Kaya-Cekin, E. Aulisa, A. Ibragimov and P. Seshaiyer, Stability Analysis of Inhomogeneous Equilibrium for Axially and Transversely Excited Nonlinear Beam, Communications on Pure and Applied Analysis, 10 (2011), 1447-1462.
doi: 10.3934/cpaa.2011.10.1447. |
[17] |
H. Koch and I. Lasiecka, Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems, Progress in Nonlinear Differential Equations and Their Applications, 50 (2002), 197-216. |
[18] |
I. Kukavica and A. Tuffaha, Solutions to a fluid-structure interaction free boundary problem, Discrete And Continuous Dynamical Systems, 32 (2012), 1355-1389.
doi: 10.3934/dcds.2012.32.1355. |
[19] |
M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill, New York, 1937.
doi: 10.1097/00010694-193808000-00008. |
[20] |
V. V. Novozhilov, Foundations of the Nonlinear Theory of Elasticity, Dover Publication, Inc., 1999. |
[21] |
N. Peake and S. V. Sorokin, A nonlinear model of the dynamics of a large elastic plate with heavy fluid loading, Proceedings: Mathematical, Physical and Engineering Sciences, 462 (2006), 2205-2224.
doi: 10.1098/rspa.2006.1673. |
[22] |
J. Peradze, A numerical alghorithm for Kirchhoff-Type nonlinear static beam, Journal of Applied Mathematics, (2009), 12 pp.
doi: 10.1155/2009/818269. |
[23] |
A. Quaini, S. Canic, R. Glowinski, S. Igo, C. Hartley, W. Zoghbi and S. Little, Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture, Journal of Biomechanic, 45 (2012), 310-318.
doi: 10.1016/j.jbiomech.2011.10.020. |
[24] |
M. Sathyamoorthy, Nonlinear Analysis of Structures, CRC, 1998. |
[25] |
SIAM PDE Conference 2011 San-Diego, Book of Abstracts, http://www.siam.org/meetings/pd11/pd11_abstracts.pdf. |
show all references
References:
[1] |
E. Aulisa, L. Bloshanskaya and A. Ibragimov, Long-term dynamics for well productivity index for nonlinear flows in porous media, Journal of Mathematical Physics, 52 (2011), 023506, 26 pp.
doi: 10.1063/1.3536463. |
[2] |
E. Aulisa, A. Cervone, S. Manservisi and P. Seshaiyer, A multilevel domain decomposition approach for studying coupled flow application, Communications in Computational Physics, 6 (2009), 319-341.
doi: 10.4208/cicp.2009.v6.p319. |
[3] |
M. Boulakia and S. Guerrero, A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations, Ann. Inst. H. Poincare Anal. Non Lineaire, 26 (2009), 777-813.
doi: 10.1016/j.anihpc.2008.02.004. |
[4] |
I. D. Chueshov, A global attractor for a fluid-plate interaction model accounting only for longitudinal deformations of the plate, Mathematical Methods in the Applied Sciences, 34 (2011), 1801-1812.
doi: doi:10.1002/mma.1496. |
[5] |
D. Coutand and S. Shkoller, Motion of an elastic solid inside an incompressible viscous fluid, Arch. Ration. Mech. Anal., 176 (2005), 25-102.
doi: 10.1007/s00205-004-0340-7. |
[6] |
Q. Du, M. D. Gunzburger, L. S. Hou and J. Lee, Analysis of a linear fluid-structure interaction problem, Discrete and Continuous Dynamical Systems, 9 (2003), 633-650.
doi: 10.3934/dcds.2003.9.633. |
[7] |
F. Flori and P. Orenga, Fluid-structure interaction: Analysis of a 3-D compressible model, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 17 (2000), 753-777.
doi: 10.1016/S0294-1449(00)00119-0. |
[8] |
D. G. Gorman, I. Trendafilova, A. J. Mulholland and J. Horacek, Analytical modeling and extraction of the modal behavior of a cantilever beam in fluid interaction, Journal of Sound and Vibration, 308 (2007), 231-245.
doi: 10.1016/j.jsv.2007.07.032. |
[9] |
C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, SIAM Journal on Mathematical Analysis, 40 (2008), 716-737.
doi: 10.1137/070699196. |
[10] |
M. Grobbelaar Van Dalsen, On a fluid-structure model in which the dynamics of the structure involves the shear stress due to the fluid, Journal of Mathematical Fluid Mechanics, 10 (2008), 388-401.
doi: 10.1007/s00021-006-0236-4. |
[11] |
M. Grobbelaar Van Dalsen, Strong stability for a fluid structure interaction model, Math. Meth. Appl. Sci., 32 (2009), 1452-1466.
doi: 10.1002/mma.1104. |
[12] |
J. Hron and S. Turek, A Monolithic FEM/ Multigrid solver for ALE formulation of fluid structure interaction with applications in biomechanics, Lecture Notes in Computational Science and Engineering, 53 (2006), 146-170.
doi: 10.1007/3-540-34596-5_7. |
[13] |
E. Kaya-Cekin, E. Aulisa and A. Ibragimov, Fluid structure interaction problem with changing thickness non-linear beam, Discrete And Continuous Dynamical Systems, Supplement, II (2011), 813-823. |
[14] |
E. Kaya-Cekin, E. Aulisa and A. Ibragimov, Stability Analysis of non-linear plates coupled with Darcy flows, Evolution Equation and Control Theory, 2 (2013), 193-232.
doi: 10.3934/eect.2013.2.193. |
[15] |
E. Kaya-Cekin, E. Aulisa, A. Ibragimov and P. Seshaiyer, A Stability Estimate for Fluid Structure Interaction Problem with Non-Linear Beam, Discrete And Continuous Dynamical Systems. Supplement, (2009), 424-432. |
[16] |
E. Kaya-Cekin, E. Aulisa, A. Ibragimov and P. Seshaiyer, Stability Analysis of Inhomogeneous Equilibrium for Axially and Transversely Excited Nonlinear Beam, Communications on Pure and Applied Analysis, 10 (2011), 1447-1462.
doi: 10.3934/cpaa.2011.10.1447. |
[17] |
H. Koch and I. Lasiecka, Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems, Progress in Nonlinear Differential Equations and Their Applications, 50 (2002), 197-216. |
[18] |
I. Kukavica and A. Tuffaha, Solutions to a fluid-structure interaction free boundary problem, Discrete And Continuous Dynamical Systems, 32 (2012), 1355-1389.
doi: 10.3934/dcds.2012.32.1355. |
[19] |
M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill, New York, 1937.
doi: 10.1097/00010694-193808000-00008. |
[20] |
V. V. Novozhilov, Foundations of the Nonlinear Theory of Elasticity, Dover Publication, Inc., 1999. |
[21] |
N. Peake and S. V. Sorokin, A nonlinear model of the dynamics of a large elastic plate with heavy fluid loading, Proceedings: Mathematical, Physical and Engineering Sciences, 462 (2006), 2205-2224.
doi: 10.1098/rspa.2006.1673. |
[22] |
J. Peradze, A numerical alghorithm for Kirchhoff-Type nonlinear static beam, Journal of Applied Mathematics, (2009), 12 pp.
doi: 10.1155/2009/818269. |
[23] |
A. Quaini, S. Canic, R. Glowinski, S. Igo, C. Hartley, W. Zoghbi and S. Little, Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture, Journal of Biomechanic, 45 (2012), 310-318.
doi: 10.1016/j.jbiomech.2011.10.020. |
[24] |
M. Sathyamoorthy, Nonlinear Analysis of Structures, CRC, 1998. |
[25] |
SIAM PDE Conference 2011 San-Diego, Book of Abstracts, http://www.siam.org/meetings/pd11/pd11_abstracts.pdf. |
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