-
Previous Article
Irreducibility and strong Feller property for stochastic evolution equations in Banach spaces
- DCDS-B Home
- This Issue
- Next Article
Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization
1. | Dipartimento di Matematica, Università di Pisa, I-56127 Pisa, Italy |
2. | Department of Civil Infrastructure and Environmental Engineering, Khalifa University of Science, Technology & Research (KUSTAR), Abu Dhabi, United Arab Emirates |
3. | Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, United States |
References:
[1] |
N. A. Adams and S. Stolz, Deconvolution Methods for Subgrid-Scale Approximation in Large Eddy Simulation,, Modern Simulation Strategies for Turbulent Flow, (2001). Google Scholar |
[2] |
N. A. Adams and S. Stolz, A subgrid-scale deconvolution approach for shock capturing,, J. Comput. Phys., 178 (2002), 391.
doi: 10.1006/jcph.2002.7034. |
[3] |
H. Beirão da Veiga, Time periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains-Leray's problem for periodic flows,, Arch. Ration. Mech. Anal., 178 (2005), 301.
doi: 10.1007/s00205-005-0376-3. |
[4] |
L. C. Berselli, Analysis of a Large Eddy Simulation model based on anisotropic filtering,, J. Math. Anal. Appl., 386 (2012), 149.
doi: 10.1016/j.jmaa.2011.07.044. |
[5] |
L. C. Berselli, Towards fluid equations by approximate deconvolution models,, in Mathematical Aspects of Fluid Mechanics, (2012), 1.
|
[6] |
L. C. Berselli and L. Bisconti, On the structural stability of the Euler-Voigt and Navier-Stokes-Voigt models,, Nonlinear Anal., 75 (2012), 117.
doi: 10.1016/j.na.2011.08.011. |
[7] |
L. C. Berselli, F. Guerra, B. Mazzolai and E. Sinibaldi, Pulsatile viscous flows in elliptical vessels and annuli: solution to the inverse problem, with application to blood and cerebrospinal fluid flow,, SIAM J. Appl. Math., 74 (2014), 40.
doi: 10.1137/120903385. |
[8] |
L. C. Berselli, T. Iliescu and W. J. Layton, Mathematics of Large Eddy Simulation of Turbulent Flows,, Scientific Computation, (2006).
doi: 10.1007/b137408. |
[9] |
L. C. Berselli and R. Lewandowski, Convergence of approximate deconvolution models to the mean Navier-Stokes equations,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 171.
doi: 10.1016/j.anihpc.2011.10.001. |
[10] |
L. C. Berselli and S. Spirito, On the Construction of Suitable Weak Solutions to the 3D Navier-Stokes Equations in a Bounded Domain by an Artificial Compressibility Method,, Technical Report 1504.07800, (1504). Google Scholar |
[11] |
A. L. Bowers, T.-Y. Kim, M. Neda, L. G. Rebholz and E. Fried, The Leray-$\alpha\beta$-deconvolution model: Energy analysis and numerical algorithms,, Appl. Math. Model., 37 (2013), 1225.
doi: 10.1016/j.apm.2012.03.040. |
[12] |
Y. Cao, E. M. Lunasin and E. S. Titi, Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models,, Commun. Math. Sci., 4 (2006), 823.
doi: 10.4310/CMS.2006.v4.n4.a8. |
[13] |
R. W. Carroll and R. E. Showalter, Singular and Degenerate Cauchy Problems,, Academic Press [Harcourt Brace Jovanovich, (1976).
|
[14] |
T. Chacón Rebollo and R. Lewandowski, Mathematical and Numerical Foundations of Turbulence Models and Applications,, Modeling and Simulation in Science, (2014).
doi: 10.1007/978-1-4939-0455-6. |
[15] |
S. Chen, G. Doolen, R. Kraichnan and Z. She, On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence,, Phys. Fluids A, 5 (1993), 458.
doi: 10.1063/1.858897. |
[16] |
S. Chen, D. D. Holm, L. G. Margolin and R. Zhang, Direct numerical simulations of the Navier-Stokes alpha model,, Phys. D, 133 (1999), 66.
doi: 10.1016/S0167-2789(99)00099-8. |
[17] |
A. Cheskidov, D. D. Holm, E. Olson and E. S. Titi, On a Leray-$\alpha$ model of turbulence,, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461 (2005), 629.
doi: 10.1098/rspa.2004.1373. |
[18] |
A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows,, SIAM J. Math. Anal., 37 (2006), 1890.
doi: 10.1137/S0036141003436302. |
[19] |
A. A. Dunca, A two-level multiscale deconvolution method for the large eddy simulation of turbulent flows,, Math. Models Methods Appl. Sci., 22 (2012).
doi: 10.1142/S0218202512500017. |
[20] |
C. Foias, D. D. Holm and E. S. Titi, The Navier-Stokes-alpha model of fluid turbulence,, Phys. D, 152/153 (2001), 505.
doi: 10.1016/S0167-2789(01)00191-9. |
[21] |
C. Foias, O. Manley, R. Rosa and R. Temam, Navier-Stokes Equations and Turbulence, vol. 83 of Encyclopedia of Mathematics and its Applications,, Cambridge University Press, (2001).
doi: 10.1017/CBO9780511546754. |
[22] |
U. Frisch, Turbulence, The Legacy of A.N. Kolmogorov,, Cambridge University Press, (1995).
|
[23] |
Y. C. Fung, Biomechanics. Circulation,, Springer-Verlag, (1997). Google Scholar |
[24] |
K. J. Galvin, L. G. Rebholz and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models,, SIAM J. Numer. Anal., 52 (2014), 678.
doi: 10.1137/120887412. |
[25] |
D. F. Hinz, T.-Y. Kim and E. Fried, Statistics of the Navier-Stokes-alpha-beta regularization model for fluid turbulence,, J. Phys. A, 47 (2014).
doi: 10.1088/1751-8113/47/5/055501. |
[26] |
K. J. K. Galvin, Advancements in Finite Element Methods for Newtonian and Non-Newtonian Flows,, PhD thesis, (2013).
|
[27] |
V. K. Kalantarov, B. Levant and E. S. Titi, Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations,, J. Nonlinear Sci., 19 (2009), 133.
doi: 10.1007/s00332-008-9029-7. |
[28] |
V. K. Kalantarov and E. S. Titi, Global attractors and determining modes for the 3D Navier-Stokes-Voight equations,, Chin. Ann. Math. Ser. B, 30 (2009), 697.
doi: 10.1007/s11401-009-0205-3. |
[29] |
T.-Y. Kim, M. Cassiani, J. D. Albertson, J. E. Dolbow, E. Fried and M. E. Gurtin, Impact of the inherent separation of scales in the Navier-Stokes-$\alpha\beta$ equations,, Phys. Rev. E (3), 79 (2009).
doi: 10.1103/PhysRevE.79.045307. |
[30] |
T.-Y. Kim, L. G. Rebholz and E. Fried, A deconvolution enhancement of the Navier-Stokes-$\alpha\beta$ model,, J. Comput. Phys., 231 (2012), 4015.
doi: 10.1016/j.jcp.2011.12.003. |
[31] |
P. Kuberry, A. Larios, L. G. Rebholz and N. E. Wilson, Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows,, Comput. Math. Appl., 64 (2012), 2647.
doi: 10.1016/j.camwa.2012.07.010. |
[32] |
A. Larios, The Inviscid Voigt-Regularization for Hydrodynamic Models: Global Regularity, Boundary Conditions, and Blow-Up Phenomena,, PhD thesis, (2011).
|
[33] |
A. Larios and E. S. Titi, On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models,, Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 603.
doi: 10.3934/dcdsb.2010.14.603. |
[34] |
W. J. Layton and R. Lewandowski, On a well-posed turbulence model,, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 111.
doi: 10.3934/dcdsb.2006.6.111. |
[35] |
W. J. Layton and L. Rebholz, Approximate Deconvolution Models of Turbulence Approximate Deconvolution Models of Turbulence, vol. 2042 of Lecture Notes in Mathematics,, Springer, (2012).
doi: 10.1007/978-3-642-24409-4. |
[36] |
B. Levant, F. Ramos and E. S. Titi, On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model,, Commun. Math. Sci., 8 (2010), 277.
doi: 10.4310/CMS.2010.v8.n1.a14. |
[37] |
A. P. Oskolkov, The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers,, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 38 (1973), 98.
|
[38] |
A. P. Oskolkov, On the theory of unsteady flows of Kelvin-Voigt fluids,, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 115 (1982), 191.
|
[39] |
A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system,, in Handbook of numerical analysis. Vol. XII, (2004), 3.
doi: 10.1016/S1570-8659(03)12001-7. |
[40] |
L. G. Rebholz, Well-posedness of a reduced order approximate deconvolution turbulence model,, J. Math. Anal. Appl., 405 (2013), 738.
doi: 10.1016/j.jmaa.2013.04.036. |
[41] |
P. Sagaut, Large Eddy Simulation for Incompressible Flows,, Scientific Computation, (2001).
doi: 10.1007/978-3-662-04416-2. |
[42] |
Z. S. She, E. Jackson and S. A. Orszag, Statistical aspects of vortex dynamics in turbulence,, in New perspectives in turbulence (Newport, (1989), 315.
doi: 10.1007/978-1-4612-3156-1_12. |
[43] |
I. Stanculescu and C. C. Manica, Numerical analysis of Leray-Tikhonov deconvolution models of fluid motion,, Comput. Math. Appl., 60 (2010), 1440.
doi: 10.1016/j.camwa.2010.06.026. |
[44] |
S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation,, Phys. Fluids, 11 (1999), 1699.
doi: 10.1063/1.869867. |
[45] |
S. Stolz, N. A. Adams and L. Kleiser, An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows,, Phys. Fluids, 13 (2001), 997.
doi: 10.1063/1.1350896. |
[46] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences,, 2nd edition, (1997).
doi: 10.1007/978-1-4612-0645-3. |
[47] |
J. R. Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known,, J. Physiol., 127 (1955), 553.
doi: 10.1113/jphysiol.1955.sp005276. |
show all references
References:
[1] |
N. A. Adams and S. Stolz, Deconvolution Methods for Subgrid-Scale Approximation in Large Eddy Simulation,, Modern Simulation Strategies for Turbulent Flow, (2001). Google Scholar |
[2] |
N. A. Adams and S. Stolz, A subgrid-scale deconvolution approach for shock capturing,, J. Comput. Phys., 178 (2002), 391.
doi: 10.1006/jcph.2002.7034. |
[3] |
H. Beirão da Veiga, Time periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains-Leray's problem for periodic flows,, Arch. Ration. Mech. Anal., 178 (2005), 301.
doi: 10.1007/s00205-005-0376-3. |
[4] |
L. C. Berselli, Analysis of a Large Eddy Simulation model based on anisotropic filtering,, J. Math. Anal. Appl., 386 (2012), 149.
doi: 10.1016/j.jmaa.2011.07.044. |
[5] |
L. C. Berselli, Towards fluid equations by approximate deconvolution models,, in Mathematical Aspects of Fluid Mechanics, (2012), 1.
|
[6] |
L. C. Berselli and L. Bisconti, On the structural stability of the Euler-Voigt and Navier-Stokes-Voigt models,, Nonlinear Anal., 75 (2012), 117.
doi: 10.1016/j.na.2011.08.011. |
[7] |
L. C. Berselli, F. Guerra, B. Mazzolai and E. Sinibaldi, Pulsatile viscous flows in elliptical vessels and annuli: solution to the inverse problem, with application to blood and cerebrospinal fluid flow,, SIAM J. Appl. Math., 74 (2014), 40.
doi: 10.1137/120903385. |
[8] |
L. C. Berselli, T. Iliescu and W. J. Layton, Mathematics of Large Eddy Simulation of Turbulent Flows,, Scientific Computation, (2006).
doi: 10.1007/b137408. |
[9] |
L. C. Berselli and R. Lewandowski, Convergence of approximate deconvolution models to the mean Navier-Stokes equations,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 171.
doi: 10.1016/j.anihpc.2011.10.001. |
[10] |
L. C. Berselli and S. Spirito, On the Construction of Suitable Weak Solutions to the 3D Navier-Stokes Equations in a Bounded Domain by an Artificial Compressibility Method,, Technical Report 1504.07800, (1504). Google Scholar |
[11] |
A. L. Bowers, T.-Y. Kim, M. Neda, L. G. Rebholz and E. Fried, The Leray-$\alpha\beta$-deconvolution model: Energy analysis and numerical algorithms,, Appl. Math. Model., 37 (2013), 1225.
doi: 10.1016/j.apm.2012.03.040. |
[12] |
Y. Cao, E. M. Lunasin and E. S. Titi, Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models,, Commun. Math. Sci., 4 (2006), 823.
doi: 10.4310/CMS.2006.v4.n4.a8. |
[13] |
R. W. Carroll and R. E. Showalter, Singular and Degenerate Cauchy Problems,, Academic Press [Harcourt Brace Jovanovich, (1976).
|
[14] |
T. Chacón Rebollo and R. Lewandowski, Mathematical and Numerical Foundations of Turbulence Models and Applications,, Modeling and Simulation in Science, (2014).
doi: 10.1007/978-1-4939-0455-6. |
[15] |
S. Chen, G. Doolen, R. Kraichnan and Z. She, On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence,, Phys. Fluids A, 5 (1993), 458.
doi: 10.1063/1.858897. |
[16] |
S. Chen, D. D. Holm, L. G. Margolin and R. Zhang, Direct numerical simulations of the Navier-Stokes alpha model,, Phys. D, 133 (1999), 66.
doi: 10.1016/S0167-2789(99)00099-8. |
[17] |
A. Cheskidov, D. D. Holm, E. Olson and E. S. Titi, On a Leray-$\alpha$ model of turbulence,, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461 (2005), 629.
doi: 10.1098/rspa.2004.1373. |
[18] |
A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows,, SIAM J. Math. Anal., 37 (2006), 1890.
doi: 10.1137/S0036141003436302. |
[19] |
A. A. Dunca, A two-level multiscale deconvolution method for the large eddy simulation of turbulent flows,, Math. Models Methods Appl. Sci., 22 (2012).
doi: 10.1142/S0218202512500017. |
[20] |
C. Foias, D. D. Holm and E. S. Titi, The Navier-Stokes-alpha model of fluid turbulence,, Phys. D, 152/153 (2001), 505.
doi: 10.1016/S0167-2789(01)00191-9. |
[21] |
C. Foias, O. Manley, R. Rosa and R. Temam, Navier-Stokes Equations and Turbulence, vol. 83 of Encyclopedia of Mathematics and its Applications,, Cambridge University Press, (2001).
doi: 10.1017/CBO9780511546754. |
[22] |
U. Frisch, Turbulence, The Legacy of A.N. Kolmogorov,, Cambridge University Press, (1995).
|
[23] |
Y. C. Fung, Biomechanics. Circulation,, Springer-Verlag, (1997). Google Scholar |
[24] |
K. J. Galvin, L. G. Rebholz and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models,, SIAM J. Numer. Anal., 52 (2014), 678.
doi: 10.1137/120887412. |
[25] |
D. F. Hinz, T.-Y. Kim and E. Fried, Statistics of the Navier-Stokes-alpha-beta regularization model for fluid turbulence,, J. Phys. A, 47 (2014).
doi: 10.1088/1751-8113/47/5/055501. |
[26] |
K. J. K. Galvin, Advancements in Finite Element Methods for Newtonian and Non-Newtonian Flows,, PhD thesis, (2013).
|
[27] |
V. K. Kalantarov, B. Levant and E. S. Titi, Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations,, J. Nonlinear Sci., 19 (2009), 133.
doi: 10.1007/s00332-008-9029-7. |
[28] |
V. K. Kalantarov and E. S. Titi, Global attractors and determining modes for the 3D Navier-Stokes-Voight equations,, Chin. Ann. Math. Ser. B, 30 (2009), 697.
doi: 10.1007/s11401-009-0205-3. |
[29] |
T.-Y. Kim, M. Cassiani, J. D. Albertson, J. E. Dolbow, E. Fried and M. E. Gurtin, Impact of the inherent separation of scales in the Navier-Stokes-$\alpha\beta$ equations,, Phys. Rev. E (3), 79 (2009).
doi: 10.1103/PhysRevE.79.045307. |
[30] |
T.-Y. Kim, L. G. Rebholz and E. Fried, A deconvolution enhancement of the Navier-Stokes-$\alpha\beta$ model,, J. Comput. Phys., 231 (2012), 4015.
doi: 10.1016/j.jcp.2011.12.003. |
[31] |
P. Kuberry, A. Larios, L. G. Rebholz and N. E. Wilson, Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows,, Comput. Math. Appl., 64 (2012), 2647.
doi: 10.1016/j.camwa.2012.07.010. |
[32] |
A. Larios, The Inviscid Voigt-Regularization for Hydrodynamic Models: Global Regularity, Boundary Conditions, and Blow-Up Phenomena,, PhD thesis, (2011).
|
[33] |
A. Larios and E. S. Titi, On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models,, Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 603.
doi: 10.3934/dcdsb.2010.14.603. |
[34] |
W. J. Layton and R. Lewandowski, On a well-posed turbulence model,, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 111.
doi: 10.3934/dcdsb.2006.6.111. |
[35] |
W. J. Layton and L. Rebholz, Approximate Deconvolution Models of Turbulence Approximate Deconvolution Models of Turbulence, vol. 2042 of Lecture Notes in Mathematics,, Springer, (2012).
doi: 10.1007/978-3-642-24409-4. |
[36] |
B. Levant, F. Ramos and E. S. Titi, On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model,, Commun. Math. Sci., 8 (2010), 277.
doi: 10.4310/CMS.2010.v8.n1.a14. |
[37] |
A. P. Oskolkov, The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers,, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 38 (1973), 98.
|
[38] |
A. P. Oskolkov, On the theory of unsteady flows of Kelvin-Voigt fluids,, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 115 (1982), 191.
|
[39] |
A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system,, in Handbook of numerical analysis. Vol. XII, (2004), 3.
doi: 10.1016/S1570-8659(03)12001-7. |
[40] |
L. G. Rebholz, Well-posedness of a reduced order approximate deconvolution turbulence model,, J. Math. Anal. Appl., 405 (2013), 738.
doi: 10.1016/j.jmaa.2013.04.036. |
[41] |
P. Sagaut, Large Eddy Simulation for Incompressible Flows,, Scientific Computation, (2001).
doi: 10.1007/978-3-662-04416-2. |
[42] |
Z. S. She, E. Jackson and S. A. Orszag, Statistical aspects of vortex dynamics in turbulence,, in New perspectives in turbulence (Newport, (1989), 315.
doi: 10.1007/978-1-4612-3156-1_12. |
[43] |
I. Stanculescu and C. C. Manica, Numerical analysis of Leray-Tikhonov deconvolution models of fluid motion,, Comput. Math. Appl., 60 (2010), 1440.
doi: 10.1016/j.camwa.2010.06.026. |
[44] |
S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation,, Phys. Fluids, 11 (1999), 1699.
doi: 10.1063/1.869867. |
[45] |
S. Stolz, N. A. Adams and L. Kleiser, An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows,, Phys. Fluids, 13 (2001), 997.
doi: 10.1063/1.1350896. |
[46] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences,, 2nd edition, (1997).
doi: 10.1007/978-1-4612-0645-3. |
[47] |
J. R. Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known,, J. Physiol., 127 (1955), 553.
doi: 10.1113/jphysiol.1955.sp005276. |
[1] |
Yila Bai, Haiqing Zhao, Xu Zhang, Enmin Feng, Zhijun Li. The model of heat transfer of the arctic snow-ice layer in summer and numerical simulation. Journal of Industrial & Management Optimization, 2005, 1 (3) : 405-414. doi: 10.3934/jimo.2005.1.405 |
[2] |
Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method. Mathematical Biosciences & Engineering, 2011, 8 (2) : 263-277. doi: 10.3934/mbe.2011.8.263 |
[3] |
Christopher Bose, Rua Murray. Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 597-615. doi: 10.3934/dcds.2006.14.597 |
[4] |
Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018 |
[5] |
Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
[6] |
Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 |
[7] |
Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016 |
[8] |
Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic & Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053 |
[9] |
Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817 |
[10] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
[11] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[12] |
Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 |
[13] |
Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 |
[14] |
Zhi-Min Chen, Philip A. Wilson. Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2329-2341. doi: 10.3934/dcdsb.2012.17.2329 |
[15] |
Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042 |
[16] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[17] |
Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027 |
[18] |
Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 |
[19] |
Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]