In this paper, we study the initial-boundary value problem for the von Karman equations inside domains with moving ends. Global existence, uniqueness of solutions, and the exponential decay to the energy are established provided the initial data are bounded.
REFERENCES
1.
Avalos
, G.
, “Null controllability of von Kármán thermoelastic plates under the clamped or free mechanical boundary conditions
,” J. Math. Anal. Appl.
318
, 410
(2006
).2.
Bradley
, M. E.
and Lasiecka
, I.
, “Global decay rates for the solutions to a von Karman plate without geometric conditions
,” J. Math. Anal. Appl.
181
, 254
(1994
).3.
Benabidallah
, R.
and Ferreira
, J.
, “Asymptotic behaviour for the nonlinear beam equation in non-cylindrical domain
,” Commun. Appl. Anal.
6
, 219
(2002
).4.
Chueshov
, I.
and Lasiecka
, I.
, “Global attractors for von Karman evolutions with a nonlinear boundary dissipation
,” J. Differ. Equations
198
, 196
(2004
).5.
Favini
, A.
, Horn
, M.
, Lasiecka
, I.
, and Tataru
, D.
, “Global existence, uniqueness and regularity of solutions to a von Karman system with nonlinear boundary dissipation
,” Diff. Integral Eq.
9
, 267
(1996
).6.
Ferreira
, J.
, Santos
, M. L.
, and Matos
, M. P.
, “Stability for the beam equation with memory in non-cylindrical domain
,” Math. Methods Appl. Sci.
27
, 1493
(2004
).7.
Ferreira
, J.
, Santos
, M. L.
, Matos
, M. P.
, and Bastos
, W. D.
, “Exponential decay for Kirchhoff wave equation with nonlocal condition in a noncylindrical domain
,” Math. Comput. Modell.
39
, 1285
(2004
).8.
Khanmamedov
, A. Kh.
, “Global attractors for von Karman equations with nonlinear interior dissipation
,” J. Math. Anal. Appl.
318
, 92
(2006
).9.
Lagnese
, J.
, Boundary Stabilization of Thin Plates
(SIAM
, Philadelphia, PA
, 1989
).10.
Munoz Rivera
, J. M.
and Menzala
, G. P.
, “Uniform rates of decay for full von Karman system of dynamic viscoelasticity with memory
,” Asymptotic Anal.
27
, 335
(2001
).11.
Park
, J. Y.
and Park
, S. H.
, “Uniform decay for a von Karman plate equation with a boundary memory condition
,” Math. Methods Appl. Sci.
28
, 2225
(2005
).12.
Passo
, R. D.
and Ughi
, M.
, “Problemes de Dirichlet pour une classe d’equations paraboliques non lineaires dans des ouverts noncylindriques
,” C. R. Seances Acad. Sci., Ser. I-Math.
308
, 555
(1989
).13.
Santos
, M. L.
, Ferreira
, J.
and Raposo
, C. A.
, “Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary
,” Abstr. Appl. Anal.
2005
, 901
(2005
).14.
Santos
, M. L.
, Rocha
, M. P. C.
, and Braga
, P. L. O.
, “Global solvability and asymptotic behavior for a nonlinear coupled system of viscoelastic waves with memory in noncylindrical domain
,” J. Math. Anal. Appl.
325
, 1077
(2007
).© 2009 American Institute of Physics.
2009
American Institute of Physics
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