Global attractor for plate equation with nonlinear damping

Abstract In this paper, we study the long-time behavior of plate equation with nonlinear damping and critical nonlinearity. We prove the existence of a global attractor in the space H 0 2 ( Ω ) × L 2 ( Ω ) .

[1]  Igor Chueshov,et al.  Global Attractors for Mindlin–Timoshenko Plates and for Their Kirchhoff Limits , 2006 .

[2]  I. Lasiecka,et al.  Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models , 2006 .

[3]  Igor Chueshov,et al.  Attractors for Second-Order Evolution Equations with a Nonlinear Damping , 2004 .

[4]  Igor Chueshov,et al.  Global attractor for a composite system of nonlinear wave and plate equations , 2006 .

[5]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[6]  John M. Ball,et al.  GLOBAL ATTRACTORS FOR DAMPED SEMILINEAR WAVE EQUATIONS , 2003 .

[7]  Chengkui Zhong,et al.  Global attractors for hyperbolic equations with critical exponent in locally uniform spaces , 2006 .

[8]  A. Kh. Khanmamedov,et al.  Existence of a global attractor for the plate equation with a critical exponent in an unbounded domain , 2005, Appl. Math. Lett..

[9]  Sergey Zelik,et al.  A remark on the damped wave equation , 2006 .

[10]  Irena Lasiecka,et al.  Finite dimensionality and compactness of attractors for von Karman equations with nonlinear dissipation , 1999 .

[11]  Inertial Manifolds for von Karman Plate Equations , 2002 .

[12]  A. Khanmamedov.  Global attractors for the plate equation with a localized damping and a critical exponent in an unbounded domain , 2006 .

[13]  Igor Chueshov,et al.  Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent , 2007 .

[14]  I. Lasiecka,et al.  Long-time Behavior of Second Order Evolution Equations With Nonlinear Damping , 2008 .

[15]  I. Lasiecka,et al.  ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION , 2002 .

[16]  Finite dimensionality of the global attractors for von Karman equations with nonlinear interior dissipation , 2007 .

[17]  A.Kh. Khanmamedov,et al.  Global attractors for von Karman equations with nonlinear interior dissipation , 2006 .

[18]  R. Temam,et al.  Attractors for damped nonlinear hyperbolic equations , 1987 .

[19]  Igor Chueshov,et al.  Finite Dimensionality of the Attractor for a Semilinear Wave Equation with Nonlinear Boundary Dissipation , 2005 .

[20]  E. Zuazua,et al.  Global attractors for semilinear wave equations with locally distributed nonlinear damping and critical exponent , 1993 .

[21]  Chengkui Zhong,et al.  Global attractors for the wave equation with nonlinear damping , 2006 .

[22]  Igor Chueshov,et al.  Global attractors for von Karman evolutions with a nonlinear boundary dissipation , 2004 .

[23]  E. Feireisl,et al.  Global Attractors for Semilinear Damped Wave Equations with Supercritical Exponent , 1995 .

[24]  Igor Chueshov,et al.  Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping , 2007 .