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Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent
1.  Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara, Turkey 
References:
[1] 
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, NorthHolland Publishing Co., Amsterdam, 1992. Google Scholar 
[2] 
A. N. Carvalho and J. W. Cholewa, Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207 (2002), 287310. Google Scholar 
[3] 
I. Chueshov and S. Kolbasin, Longtime dynamics in plate models with strong nonlinear damping,, \arXiv{1010.4991}., (). Google Scholar 
[4] 
I. Chueshov and I. Lasiecka, Longtime behavior of second order evolution equations with nonlinear damping, Memoirs of AMS, 195 (2008). Google Scholar 
[5] 
M. Conti and V. Pata, On the regulariaty of global attractors, Discrete Contin. Dynam. Systems, 25 (2009), 12091217. Google Scholar 
[6] 
B. Duffy, P. Freitas and M. Grinfeld, Memory driven instability in a diffusion process, SIAM J. Math. Anal., 33 (2002), 10901106. Google Scholar 
[7] 
V. Kalantarov, Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 152 (1986), 5054. Google Scholar 
[8] 
V. Kalantarov and S. Zelik, Finitedimensional attractors for the quasilinear stronglydamped wave equation, J. Diff. Equations, 247 (2009), 11201155. Google Scholar 
[9] 
A. Kh. Khanmamedov, Global attractors for 2D wave equations with displacementdependent damping, Math. Methods Appl. Sci., 33 (2010), 177187. Google Scholar 
[10] 
A. Kh. Khanmamedov, Remark on the regularity of the global attractor for the wave equation with nonlinear damping, Nonlinear Analysis, 72 (2010), 19931999. Google Scholar 
[11] 
A. Kh. Khanmamedov, A strong global attractor for 3D wave equations with displacement dependent damping, Appl. Math. Letters, 23 (2010), 928934. Google Scholar 
[12] 
J.L. Lions and E. Magenes, "Nonhomogeneous Boundary Value Problems and Applications," 1, SpringerVerlag, New YorkHeidelberg, 1972. Google Scholar 
[13] 
W. E. Olmstead, S. H. Davis, S. Rosenblat and W. L. Kath, Bifurcation with memory, SIAM J. Appl. Math., 46 (1986), 171188. Google Scholar 
[14] 
V. Pata and M. Squassina, On the strongly damped wave equation, Commun. Math. Phys., 253 (2005), 511533. Google Scholar 
[15] 
V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 14951506. Google Scholar 
[16] 
V. Pata and S. Zelik, Global and exponential attractors for 3D wave equations with displacement dependent damping, Math. Methods Appl. Sci., 29 (2006), 12911306. Google Scholar 
[17] 
R. Temam, "InfiniteDimensional Dynamical Systems in Mechanics and Physics," Applied Mathematical Sciences, 68, SpringerVerlag, New York, 1988. Google Scholar 
[18] 
J. Simon, Compact sets in the space $L_p(0, T;B)$, Annali Mat. Pura Appl., 146 (1987), 6596. Google Scholar 
[19] 
C. Sun, D. Cao and J. Duan, Nonautonomous wave dynamics with memoryasymptotic regularity and uniform attractor, Discrete Contin. Dyn. Syst. Ser. B, 9 (2008), 743761. Google Scholar 
[20] 
M. Yang and C. Sun, Attractors for strongly damped wave equations, Nonlinear Analysis: Real World Applications, 10 (2009), 10971100. Google Scholar 
[21] 
S. Zelik, Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent, Commun. Pure Appl. Anal., 3 (2004), 921934. Google Scholar 
[22] 
S. Zhou, Global attractor for strongly damped nonlinear wave equations, Funct. Diff. Eqns., 6 (1999), 451470. Google Scholar 
show all references
References:
[1] 
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, NorthHolland Publishing Co., Amsterdam, 1992. Google Scholar 
[2] 
A. N. Carvalho and J. W. Cholewa, Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207 (2002), 287310. Google Scholar 
[3] 
I. Chueshov and S. Kolbasin, Longtime dynamics in plate models with strong nonlinear damping,, \arXiv{1010.4991}., (). Google Scholar 
[4] 
I. Chueshov and I. Lasiecka, Longtime behavior of second order evolution equations with nonlinear damping, Memoirs of AMS, 195 (2008). Google Scholar 
[5] 
M. Conti and V. Pata, On the regulariaty of global attractors, Discrete Contin. Dynam. Systems, 25 (2009), 12091217. Google Scholar 
[6] 
B. Duffy, P. Freitas and M. Grinfeld, Memory driven instability in a diffusion process, SIAM J. Math. Anal., 33 (2002), 10901106. Google Scholar 
[7] 
V. Kalantarov, Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 152 (1986), 5054. Google Scholar 
[8] 
V. Kalantarov and S. Zelik, Finitedimensional attractors for the quasilinear stronglydamped wave equation, J. Diff. Equations, 247 (2009), 11201155. Google Scholar 
[9] 
A. Kh. Khanmamedov, Global attractors for 2D wave equations with displacementdependent damping, Math. Methods Appl. Sci., 33 (2010), 177187. Google Scholar 
[10] 
A. Kh. Khanmamedov, Remark on the regularity of the global attractor for the wave equation with nonlinear damping, Nonlinear Analysis, 72 (2010), 19931999. Google Scholar 
[11] 
A. Kh. Khanmamedov, A strong global attractor for 3D wave equations with displacement dependent damping, Appl. Math. Letters, 23 (2010), 928934. Google Scholar 
[12] 
J.L. Lions and E. Magenes, "Nonhomogeneous Boundary Value Problems and Applications," 1, SpringerVerlag, New YorkHeidelberg, 1972. Google Scholar 
[13] 
W. E. Olmstead, S. H. Davis, S. Rosenblat and W. L. Kath, Bifurcation with memory, SIAM J. Appl. Math., 46 (1986), 171188. Google Scholar 
[14] 
V. Pata and M. Squassina, On the strongly damped wave equation, Commun. Math. Phys., 253 (2005), 511533. Google Scholar 
[15] 
V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 14951506. Google Scholar 
[16] 
V. Pata and S. Zelik, Global and exponential attractors for 3D wave equations with displacement dependent damping, Math. Methods Appl. Sci., 29 (2006), 12911306. Google Scholar 
[17] 
R. Temam, "InfiniteDimensional Dynamical Systems in Mechanics and Physics," Applied Mathematical Sciences, 68, SpringerVerlag, New York, 1988. Google Scholar 
[18] 
J. Simon, Compact sets in the space $L_p(0, T;B)$, Annali Mat. Pura Appl., 146 (1987), 6596. Google Scholar 
[19] 
C. Sun, D. Cao and J. Duan, Nonautonomous wave dynamics with memoryasymptotic regularity and uniform attractor, Discrete Contin. Dyn. Syst. Ser. B, 9 (2008), 743761. Google Scholar 
[20] 
M. Yang and C. Sun, Attractors for strongly damped wave equations, Nonlinear Analysis: Real World Applications, 10 (2009), 10971100. Google Scholar 
[21] 
S. Zelik, Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent, Commun. Pure Appl. Anal., 3 (2004), 921934. Google Scholar 
[22] 
S. Zhou, Global attractor for strongly damped nonlinear wave equations, Funct. Diff. Eqns., 6 (1999), 451470. Google Scholar 
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