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Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces
1. | Department of Mathematics, University of Surrey, Guildford, GU2 7XH |
References:
[1] |
C. Anh and N. Quang, Uniform attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators, Ann. Polon. Math., 98 (2010), 251-271.
doi: 10.4064/ap98-3-5. |
[2] |
A. Babin and M. Vishik, Attractors of Evolutionary Equations, North Holland, Amsterdam, 1992. |
[3] |
J. Ball, Global attractors for damped semilinear wave equations, Discrete Contin. Dyn. Syst., 10 (2004), 31-52.
doi: 10.3934/dcds.2004.10.31. |
[4] |
A. Carvalho, J. Langa and J. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, 182, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4581-4. |
[5] |
V. Chepyzhov, On uniform attractors of dynamic processes and nonautonomous equations of mathematical physics, Russian Math. Surveys, 68 (2013), 349-382. |
[6] |
V. Chepyzhov and M. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society Colloquium Publications, 49, American Mathematical Society, Providence, RI, 2002. |
[7] |
V. Chepyzhov and M. Vishik, Attractors of nonautonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333. |
[8] |
V. Chepyzhov and M. Vishik, Attractors of non-autonomous evolution equations with translation-compact symbols, in Partial Differential Operators and Mathematical Physics (Holzhau, 1994), Oper. Theory Adv. Appl., 78, Birkhäuser, Basel, 1995, 49-60. |
[9] |
H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Theory Related Fields, 100 (1994), 365-393.
doi: 10.1007/BF01193705. |
[10] |
M. Efendiev, S. Zelik and A. Miranville, Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems, Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), 703-730.
doi: 10.1017/S030821050000408X. |
[11] |
V. Kalantarov, A. Savostianov and S. Zelik, Attractors for damped quintic wave equations in bounded domains, submitted. |
[12] |
S. Lu, H. Wu and C. Zhong, Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces, Discrete Contin. Dyn. Syst., 13 (2005), 701-719.
doi: 10.3934/dcds.2005.13.701. |
[13] |
S. Lu, Attractors for nonautonomous 2D Navier-Stokes equations with less regular normal forces, J. Differential Equations, 230 (2006), 196-212.
doi: 10.1016/j.jde.2006.07.009. |
[14] |
S. Lu., Attractors for nonautonomous reaction-diffusion systems with symbols without strong translation compactness, Asymptot. Anal., 54 (2007), 197-210. |
[15] |
S. Ma, C. Zhong and H. Song, Attractors for nonautonomous 2D Navier-Stokes equations with less regular symbols, Nonlinear Anal., 71 (2009), 4215-4222.
doi: 10.1016/j.na.2009.02.107. |
[16] |
S. Ma, X. Cheng and H. Li, Attractors for non-autonomous wave equations with a new class of external forces, J. Math. Anal. Appl., 337 (2008), 808-820.
doi: 10.1016/j.jmaa.2007.03.108. |
[17] |
S. Ma and C. Zhong, The attractors for weakly damped non-autonomous hyperbolic equations with a new class of external forces, Discrete Contin. Dyn. Syst., 18 (2007), 53-70.
doi: 10.3934/dcds.2007.18.53. |
[18] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in Handbook of Differential Equations: Evolutionary Equations. Vol. IV, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008, 103-200.
doi: 10.1016/S1874-5717(08)00003-0. |
[19] |
I. Moise, R. Rosa and X. Wang, Attractors for non-compact semigroups via energy equations, Nonlinearity, 11 (1998), 1369-1393.
doi: 10.1088/0951-7715/11/5/012. |
[20] |
I. Moise, R. Rosa and X. Wang, Attractors for noncompact nonautonomous systems via energy equations, Discrete Contin. Dyn. Syst., 10 (2004), 473-496.
doi: 10.3934/dcds.2004.10.473. |
[21] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[22] |
A. Robertson and W. Robertson, Topological Vector Spaces, Reprint of the second edition, Cambridge Tracts in Mathematics, 53, Cambridge University Press, Cambridge-New York, 1980. |
[23] |
Y. Xie, K. Zhu and C. Sun, The existence of uniform attractors for non-autonomous reaction-diffusion equations on the whole space, J. Math. Phys., 53 (2012), 082703, 11 pp.
doi: 10.1063/1.4746693. |
show all references
References:
[1] |
C. Anh and N. Quang, Uniform attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators, Ann. Polon. Math., 98 (2010), 251-271.
doi: 10.4064/ap98-3-5. |
[2] |
A. Babin and M. Vishik, Attractors of Evolutionary Equations, North Holland, Amsterdam, 1992. |
[3] |
J. Ball, Global attractors for damped semilinear wave equations, Discrete Contin. Dyn. Syst., 10 (2004), 31-52.
doi: 10.3934/dcds.2004.10.31. |
[4] |
A. Carvalho, J. Langa and J. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, 182, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4581-4. |
[5] |
V. Chepyzhov, On uniform attractors of dynamic processes and nonautonomous equations of mathematical physics, Russian Math. Surveys, 68 (2013), 349-382. |
[6] |
V. Chepyzhov and M. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society Colloquium Publications, 49, American Mathematical Society, Providence, RI, 2002. |
[7] |
V. Chepyzhov and M. Vishik, Attractors of nonautonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333. |
[8] |
V. Chepyzhov and M. Vishik, Attractors of non-autonomous evolution equations with translation-compact symbols, in Partial Differential Operators and Mathematical Physics (Holzhau, 1994), Oper. Theory Adv. Appl., 78, Birkhäuser, Basel, 1995, 49-60. |
[9] |
H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Theory Related Fields, 100 (1994), 365-393.
doi: 10.1007/BF01193705. |
[10] |
M. Efendiev, S. Zelik and A. Miranville, Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems, Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), 703-730.
doi: 10.1017/S030821050000408X. |
[11] |
V. Kalantarov, A. Savostianov and S. Zelik, Attractors for damped quintic wave equations in bounded domains, submitted. |
[12] |
S. Lu, H. Wu and C. Zhong, Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces, Discrete Contin. Dyn. Syst., 13 (2005), 701-719.
doi: 10.3934/dcds.2005.13.701. |
[13] |
S. Lu, Attractors for nonautonomous 2D Navier-Stokes equations with less regular normal forces, J. Differential Equations, 230 (2006), 196-212.
doi: 10.1016/j.jde.2006.07.009. |
[14] |
S. Lu., Attractors for nonautonomous reaction-diffusion systems with symbols without strong translation compactness, Asymptot. Anal., 54 (2007), 197-210. |
[15] |
S. Ma, C. Zhong and H. Song, Attractors for nonautonomous 2D Navier-Stokes equations with less regular symbols, Nonlinear Anal., 71 (2009), 4215-4222.
doi: 10.1016/j.na.2009.02.107. |
[16] |
S. Ma, X. Cheng and H. Li, Attractors for non-autonomous wave equations with a new class of external forces, J. Math. Anal. Appl., 337 (2008), 808-820.
doi: 10.1016/j.jmaa.2007.03.108. |
[17] |
S. Ma and C. Zhong, The attractors for weakly damped non-autonomous hyperbolic equations with a new class of external forces, Discrete Contin. Dyn. Syst., 18 (2007), 53-70.
doi: 10.3934/dcds.2007.18.53. |
[18] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in Handbook of Differential Equations: Evolutionary Equations. Vol. IV, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008, 103-200.
doi: 10.1016/S1874-5717(08)00003-0. |
[19] |
I. Moise, R. Rosa and X. Wang, Attractors for non-compact semigroups via energy equations, Nonlinearity, 11 (1998), 1369-1393.
doi: 10.1088/0951-7715/11/5/012. |
[20] |
I. Moise, R. Rosa and X. Wang, Attractors for noncompact nonautonomous systems via energy equations, Discrete Contin. Dyn. Syst., 10 (2004), 473-496.
doi: 10.3934/dcds.2004.10.473. |
[21] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[22] |
A. Robertson and W. Robertson, Topological Vector Spaces, Reprint of the second edition, Cambridge Tracts in Mathematics, 53, Cambridge University Press, Cambridge-New York, 1980. |
[23] |
Y. Xie, K. Zhu and C. Sun, The existence of uniform attractors for non-autonomous reaction-diffusion equations on the whole space, J. Math. Phys., 53 (2012), 082703, 11 pp.
doi: 10.1063/1.4746693. |
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