Global attractors for strongly damped wave
equations with displacement dependent damping and nonlinear source term of
critical exponent
Pages: 119  138,
Issue 1,
September 2011
doi:10.3934/dcds.2011.31.119 Abstract
References
Full text (233.0K)
Related Articles
A. Kh. Khanmamedov  Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara, Turkey (email)
1 
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, NorthHolland Publishing Co., Amsterdam, 1992. 

2 
A. N. Carvalho and J. W. Cholewa, Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207 (2002), 287310. 

3 
I. Chueshov and S. Kolbasin, Longtime dynamics in plate models with strong nonlinear damping, arXiv:1010.4991. 

4 
I. Chueshov and I. Lasiecka, Longtime behavior of second order evolution equations with nonlinear damping, Memoirs of AMS, 195 (2008). 

5 
M. Conti and V. Pata, On the regulariaty of global attractors, Discrete Contin. Dynam. Systems, 25 (2009), 12091217. 

6 
B. Duffy, P. Freitas and M. Grinfeld, Memory driven instability in a diffusion process, SIAM J. Math. Anal., 33 (2002), 10901106. 

7 
V. Kalantarov, Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 152 (1986), 5054. 

8 
V. Kalantarov and S. Zelik, Finitedimensional attractors for the quasilinear stronglydamped wave equation, J. Diff. Equations, 247 (2009), 11201155. 

9 
A. Kh. Khanmamedov, Global attractors for 2D wave equations with displacementdependent damping, Math. Methods Appl. Sci., 33 (2010), 177187. 

10 
A. Kh. Khanmamedov, Remark on the regularity of the global attractor for the wave equation with nonlinear damping, Nonlinear Analysis, 72 (2010), 19931999. 

11 
A. Kh. Khanmamedov, A strong global attractor for 3D wave equations with displacement dependent damping, Appl. Math. Letters, 23 (2010), 928934. 

12 
J.L. Lions and E. Magenes, "Nonhomogeneous Boundary Value Problems and Applications," 1, SpringerVerlag, New YorkHeidelberg, 1972. 

13 
W. E. Olmstead, S. H. Davis, S. Rosenblat and W. L. Kath, Bifurcation with memory, SIAM J. Appl. Math., 46 (1986), 171188. 

14 
V. Pata and M. Squassina, On the strongly damped wave equation, Commun. Math. Phys., 253 (2005), 511533. 

15 
V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 14951506. 

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. 

17 
R. Temam, "InfiniteDimensional Dynamical Systems in Mechanics and Physics," Applied Mathematical Sciences, 68, SpringerVerlag, New York, 1988. 

18 
J. Simon, Compact sets in the space $L_p(0, T;B)$, Annali Mat. Pura Appl., 146 (1987), 6596. 

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. 

20 
M. Yang and C. Sun, Attractors for strongly damped wave equations, Nonlinear Analysis: Real World Applications, 10 (2009), 10971100. 

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. 

22 
S. Zhou, Global attractor for strongly damped nonlinear wave equations, Funct. Diff. Eqns., 6 (1999), 451470. 

Go to top
