Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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, North-Holland 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), 287-310.       
3 I. Chueshov and S. Kolbasin, Long-time dynamics in plate models with strong nonlinear damping, arXiv:1010.4991.
4 I. Chueshov and I. Lasiecka, Long-time 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), 1209-1217.       
6 B. Duffy, P. Freitas and M. Grinfeld, Memory driven instability in a diffusion process, SIAM J. Math. Anal., 33 (2002), 1090-1106.       
7 V. Kalantarov, Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 152 (1986), 50-54.       
8 V. Kalantarov and S. Zelik, Finite-dimensional attractors for the quasi-linear strongly-damped wave equation, J. Diff. Equations, 247 (2009), 1120-1155.       
9 A. Kh. Khanmamedov, Global attractors for 2-D wave equations with displacement-dependent damping, Math. Methods Appl. Sci., 33 (2010), 177-187.       
10 A. Kh. Khanmamedov, Remark on the regularity of the global attractor for the wave equation with nonlinear damping, Nonlinear Analysis, 72 (2010), 1993-1999.       
11 A. Kh. Khanmamedov, A strong global attractor for 3-D wave equations with displacement dependent damping, Appl. Math. Letters, 23 (2010), 928-934.       
12 J.-L. Lions and E. Magenes, "Non-homogeneous Boundary Value Problems and Applications," 1, Springer-Verlag, New York-Heidelberg, 1972.       
13 W. E. Olmstead, S. H. Davis, S. Rosenblat and W. L. Kath, Bifurcation with memory, SIAM J. Appl. Math., 46 (1986), 171-188.       
14 V. Pata and M. Squassina, On the strongly damped wave equation, Commun. Math. Phys., 253 (2005), 511-533.       
15 V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 1495-1506.       
16 V. Pata and S. Zelik, Global and exponential attractors for 3-D wave equations with displacement dependent damping, Math. Methods Appl. Sci., 29 (2006), 1291-1306.       
17 R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1988.       
18 J. Simon, Compact sets in the space $L_p(0, T;B)$, Annali Mat. Pura Appl., 146 (1987), 65-96.       
19 C. Sun, D. Cao and J. Duan, Non-autonomous wave dynamics with memory-asymptotic regularity and uniform attractor, Discrete Contin. Dyn. Syst. Ser. B, 9 (2008), 743-761.       
20 M. Yang and C. Sun, Attractors for strongly damped wave equations, Nonlinear Analysis: Real World Applications, 10 (2009), 1097-1100.       
21 S. Zelik, Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent, Commun. Pure Appl. Anal., 3 (2004), 921-934.       
22 S. Zhou, Global attractor for strongly damped nonlinear wave equations, Funct. Diff. Eqns., 6 (1999), 451-470.       

Go to top