Pullback attractors for a critical degenerate wave equation with time-dependent damping

Nonlinear Analysis: Real World Applications - Tập 63 - Trang 103421 - 2022
Dandan Li1, Qingquan Chang2, Chunyou Sun2
1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, PR China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China

Tài liệu tham khảo

B. Franchi, E. Lanconelli, Une métrique associée à une class d’opérateurs elliptiques dégénérés, in: Conference on Linear Partial and Pseudodifferential Operators, Torino, 1982, Rend. Sem. Mat. Univ. Politec., Torino 1983, 1984, pp. 105–114, (special issue). Franchi, 1983, Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients, Ann. Sc. Norm. Super. Pisa Cl. Sci., 10, 523 Franchi, 1984, An embedding theory for Sobolev spaces related to non-smooth vector fields and Harnack inequality, Comm. Partial Differential Equations, 9, 1237, 10.1080/03605308408820362 Garofalo, 1996, Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces, Comm. Pure Appl. Math., 49, 1081, 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO;2-A Lanconelli, 2000, X-elliptic operators and X-control distances, Ric. Mat., 49, 223 Gutiérrez, 2003, Maximum principle, nonhomogeous harnack inequality, and Liouville theorems for X-elliptic operators, Comm. Partial Differential Equations, 28, 1833, 10.1081/PDE-120025487 Kogoj, 2016, Hardy type inequalities for △λ-Laplacians, Complex Var. Elliptic Equ., 61, 422, 10.1080/17476933.2015.1088530 Kogoj, 2009, Liouville theorem for X-elliptic operators, Nonlinear Anal., 70, 2974, 10.1016/j.na.2008.12.029 Jeffreys, 1999 Joly, 2018, Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation, J. Math. Soc. Japan, 70, 1375, 10.2969/jmsj/77667766 Caraballo, 2010, A gradient-like nonautonomous evolution process, Internat. J. Bifur. Chaos, 20, 2751, 10.1142/S0218127410027337 Caraballo, 2011, A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor, Nonlinear Anal., 74, 2272, 10.1016/j.na.2010.11.032 Chueshov, 2008 Chepyzhov, 2002 Hale, 1988 Babin, 1992 Ball, 2004, Global attractors for damped semilinear wave equations, Discrete Contin. Dyn. Syst., 10, 31, 10.3934/dcds.2004.10.31 Kogoj, 2014, Attractors met X-elliptic operators, J. Math. Appl. Anal., 420, 407, 10.1016/j.jmaa.2014.05.070 Kogoj, 2013, Attractor for a class of semi-linear degenerate parablic equations, J. Evol. Equ., 13, 675, 10.1007/s00028-013-0196-0 Li, 2017, Global attractor for degenerate damped hyperbolic equations, J. Math. Anal. Appl., 453, 1, 10.1016/j.jmaa.2017.03.077 Carvalho, 2013 Chueshov, 2015 Adams, 1975 Cholewa, 2000 Chueshov, 2007, Long-time dynamics of von Karman semi-flow with non-linear boundary/interior damping, J. Differential Equations, 233, 42, 10.1016/j.jde.2006.09.019 Sun, 2006, Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity, Nonlinearity, 19, 2645, 10.1088/0951-7715/19/11/008 Ma, 2017, Dynamics of wave equations with moving boundary, J. Differential Equations, 262, 3317, 10.1016/j.jde.2016.11.030