Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation

P. Bergeret, 1997, <em>Classification of smooth solutions to $2\times 2$ hyperbolic systems with boundary damping</em>,, Math. Methods Appl. Sci., 20, 1563, 10.1002/(SICI)1099-1476(199712)20:18<1563::AID-MMA925>3.0.CO;2-9

M. E. Bradley, 2001, <em>Bilinear spatial control of the velocity term in a Kirchhoff plate equation</em>,, Electronic J. Differential Equations, 2001, 1

C. Buriol, 2006, <em>Energy decay rates for the Timoshenko system of thermoelastic plates</em>,, Nonlinear Analysis, 64, 92, 10.1016/j.na.2005.06.010

R. C. Charão, 2008, <em>Asymptotic behavior for a dissipative plate equation in $\R^N$ with periodic coefficients</em>,, Electronic J. Differential Equations, 2008

C. R. da Luz, 2009, <em>Asymptotic properties for a semi-linear plate equation in unbounded domains</em>,, J. Hyperbolic Differential Equations, 6, 269, 10.1142/S0219891609001824

Darmawijoyo, 2002, <em>On boundary damping for a weakly nonlinear wave equation</em>,, Nonlinear Dynamics, 30, 179, 10.1023/A:1020473930223

R. Denk, 2009, <em>$L^p$ theory for the linear thermoelastic plate equations in bounded and exterior domains</em>,, Adv. Differential Equations, 14, 685, 10.57262/ade/1355867231

W. Desch, 1996, <em>Passive boundary damping of viscoelastic structures</em>,, J. Integral Equations Appl., 8, 125, 10.1216/jiea/1181075934

G. G. Doronin, 1998, <em>A hyperbolic problem with nonlinear second-order boundary damping</em>,, Electron J. Differential Equations, 1998, 1

A. D. Drozdov, 1994, "Stability in Viscoelasticity,", North-Holland Series in Applied Mathematics and Mechanics, 38

Y. Enomoto, 2002, <em>On a thermoelastic plate equation in an exterior domain</em>,, Math. Meth. Appl. Sci., 25, 443, 10.1002/mma.290

M. Fabrizio, 1991, <em>On the existence and the asymptotic stability of solutions for linear viscoelastic solids</em>,, Arch. Rational Mech. Anal., 116, 139, 10.1007/BF00375589

T. Hosono, 2006, <em>Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system</em>,, Math. Models Meth. Appl. Sci., 16, 1839, 10.1142/S021820250600173X

K. Ide, 2008, <em>Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system</em>,, Math. Models Meth. Appl. Sci., 18, 1001, 10.1142/S0218202508002930

I. Lasiecka, 2008, <em>Existence and exponential decay of solutions to a quasilinear thermoelastic plate system</em>,, Nonlinear Differ. Equ. Appl., 15, 689, 10.1007/s00030-008-0011-8

I. Lasiecka, 1999, <em>Global solvability and uniform decays of solutions to quasilinear equation with nonlinear boundary dissipation</em>,, Comm. Partial Differential Equations, 24, 2069, 10.1080/03605309908821495

H. J. Lee, 2006, <em>Uniform decay for solution of the plate equation with a boundary condition of memory type</em>,, Trends in Math., 9, 51

W. Liu, 1998, <em>Local boundary controllability for the semi-linear plate equation</em>,, Comm. Partial Differential Equations, 23, 201

Y. Liu, 2008, <em>The point-wise estimates of solutions for dissipative wave equation in multi-dimensions</em>,, Discrete Continuous Dynam. Systems - A, 20, 1013, 10.3934/dcds.2008.20.1013

Z. Liu, 1996, <em>On the exponential stability of linear viscoelasticity and thermo-viscoelasticity</em>,, Quart. Appl. Math., 54, 21, 10.1090/qam/1373836

Z. Liu, 1999, "Semi-Groups Associated With Dissipative Systems,", Chapman $&$ Hall/CRC Research Notes in Mathematics, 398

J. R. Luyo Sánchez, 2003, "O Sistema Dinámico de von Kármán en DomÍNios NÁO Limitados é Globalmente bem Posto no Sentido de Hadamard: Análise do seu Limite Singular,", Ph.D Thesis

A. Matsumura, 1976, <em>On the asymptotic behavior of semi-linear wave equations</em>,, Publ. Res. Inst. Math. Sci., 12, 169, 10.2977/prims/1195190962

J. E. Muñoz Rivera, 2003, <em>Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory</em>,, J. Math. Anal. Appl., 286, 692, 10.1016/S0022-247X(03)00511-0

J. E. Muñoz Rivera, 2003, <em>Global stability for damped Timoshenko systems</em>,, Discrete Continuous Dynam. Systems, 9, 1625, 10.3934/dcds.2003.9.1625

J. E. Muñoz Rivera, 1994, <em>Asymptotic behavior in linear viscoelasticity</em>,, Quart. Appl. Math., 52, 628, 10.1090/qam/1306041

K. Nishihara, 2003, <em>$L^p-L^q$ estimates of solutions to the damped wave equation in $3$-dimensional space and their applications</em>,, Math. Z., 244, 631, 10.1007/s00209-003-0516-0

J. Y. Park, 2006, <em>Bilinear boundary optimal control of the velocity terms in a Kirchhoff plate equation</em>,, Trends in Math., 9, 41

A. F. Pazoto, 2004, <em>Asymptotic stability of semi-groups associated to linear weak dissipative systems</em>,, Math. Comput. Modeling, 40, 387, 10.1016/j.mcm.2003.10.048

G. P. Menzala, 2000, <em>Timoshenko's plate equations as a singular limit of the dynamical von Kármán system</em>,, J. Math. Pures Appl., 79, 73, 10.1016/S0021-7824(00)00149-5

Y. Sugitani, <em>Decay estimates of solutions to a semi-linear dissipative plate equation</em>,, J. Hyperbolic Differential Equations

R. Teman, 1979, "Navier-Stokes Equations,", Studies in Mathematics and Its Applications, 2

G. Todorova, 2000, <em>Critical exponent for a nonlinear wave equation with damping</em>,, J. Differential Equations, 174, 464, 10.1006/jdeq.2000.3933

G. Todorova, 2007, <em>The energy decay problem for wave equations with nonlinear dissipative terms in</em> $\R^n$,, Indiana University Mathematics Journal, 56, 389, 10.1512/iumj.2007.56.2963

M. A. Zarubinskaya, 2006, <em>On aspects of boundary damping for a rectangular plate</em>,, Journal of Sound and Vibration, 292, 844, 10.1016/j.jsv.2005.09.008

M. A. Zarubinskaya, 2005, <em>On aspects of asymptotic for plate equations</em>,, Nonlinear Dynamics, 41, 403, 10.1007/s11071-005-1396-0

X. Zhang, 2008, <em>On the optimality of the observability inequalities for Kirchhoff plate systems with potentials in unbounded domains</em>,, in, 233, 10.1007/978-3-540-75712-2_19