@article{AFST_1999_6_8_1_173_0,
author = {Carlos Frederico Vasconcellos and Lucia Maria Teixeira},
title = {Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {173--193},
year = {1999},
publisher = {Universit\'e Paul Sabatier},
address = {Toulouse},
volume = {Ser. 6, 8},
number = {1},
doi = {10.5802/afst.928},
mrnumber = {1721550},
zbl = {0955.35055},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.928/}
}
TY - JOUR AU - Carlos Frederico Vasconcellos AU - Lucia Maria Teixeira TI - Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 1999 SP - 173 EP - 193 VL - 8 IS - 1 PB - Université Paul Sabatier PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.928/ DO - 10.5802/afst.928 LA - en ID - AFST_1999_6_8_1_173_0 ER -
%0 Journal Article %A Carlos Frederico Vasconcellos %A Lucia Maria Teixeira %T Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 1999 %P 173-193 %V 8 %N 1 %I Université Paul Sabatier %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.928/ %R 10.5802/afst.928 %G en %F AFST_1999_6_8_1_173_0
Carlos Frederico Vasconcellos; Lucia Maria Teixeira. Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 8 (1999) no. 1, pp. 173-193. doi: 10.5802/afst.928
[1] ), ), ) and ) .- On exponential stability for von Kármán equations in the presence of thermal effects, Math. Methods in the Applied Science 21 (1998), pp. 393-416. | Zbl | MR
[2] ) .- Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl. 29 (1970), pp. 443-454. | Zbl | MR
[3] ) .- Nonlinear vibrations of beams and rectangular plates, Z. Angew Math. Phys. 15 (1964), pp. 167-175. | Zbl | MR
[4] ) .- Semilinear Hyperbolic Problems in Bounded Domains, Math. reports 3, Part 1, Harwood Academic Publishers, Gordon & Breach (1987). | Zbl
[5] ) .- Nonlinear boundary stabilization of a von Kármán plate equation, Lecture Notes in Pure and Appl. Math. 152 (1994), pp. 581-604. | Zbl | MR
[6] ) and ) .- Global existence and uniqueness of regular solutions to the dynamic von Kármán system with nonlinear boundary dissipation, Lecture Notes in Pure and Appl. Math. 165 (1994), pp. 99-119. | Zbl | MR
[7] ) .- Exact Controllabilty and Stabilization. The Multiplier Method, RAM, Masson and John Willey (1994). | Zbl | MR
[8] ) .- Modelling and stabilization of nonlinear plates, Int. Ser. of Numerical Math. 100 (1991), pp. 247-264. | Zbl | MR
[9] ) .- Boundary Stabilization of Thin Plates, SIAM Studies in Applied Mathematics. Philadelphia (1989). | Zbl | MR
[10] ) and ) .- Uniform stabilization of a nonlinear beam by nonlinear boundary feedback, J. Diff. Eqs 91 (1991), pp. 355-388. | Zbl | MR
[11] ), ), ), ), ) and ) . - On the nonlinear vibrations equation with a coefficient containing an integral, Comp. Maths Math. Phys. 33, n° 9 (1993), pp. 1171-1178. | Zbl | MR
[12] ) .- Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary, J. Diff. Eqs 79 (1989), pp. 340-381. | Zbl | MR
[13] ) and ) .- Uniform stabilization of the wave equation with Dirichlet feedback control without geometrical conditions, Appl. Math. Optim. 25 (1992), pp. 189-224. | Zbl | MR
[14] ) . - On Some Questions in Boundary Value Problems of Mathematical Physics, in: International Symposium on Continuum Mechanics and Partial Differential Equations, North-Holland (1978). | Zbl | MR
[15] ) .- On a new class of nonlinear wave equations, J. Math. Anal. and Appl. 69 (1979), pp. 252-262. | Zbl | MR
[16] ) and ) .- On a nonlinear wave equations with damping, Revista Matematica de la Universidad Complutense de Madrid 3, n° 2 (1990), pp. 213-231. | Zbl | EuDML | MR
[17] ) . - On classical solutions of a quasi-linear hyperbolic equations, Nonlinear Anal. 3 (1979), pp. 613-627. | Zbl | MR
[18] ) and ). .- Explicit exponential decay rates for solutions of von Kármán system of thermoelastic plates, Differential and Integral Equation 11 (1998), pp. 755-770. | Zbl | MR
[19] ) and ) .- Nonlinear Oscillations, John Willey (1979). | Zbl | MR
[20] ) . - On a class of quasilinear hyperbolic equations, Math. Sb. 25 (1975), pp. 145-158. | Zbl | MR
[21] ) and ) .- Boundary stabilization of the von Kármán equations, SIAM J. Control and Opt. 33 (1995), pp. 255-273. | Zbl | MR
[22] ) .- On local strong solutions of a nonlinear partial differential equation, Applicable Analysis 10 (1980), pp. 93-104. | Zbl | MR
[23] ) . - The Energy Method in Nonlinear Partial Differential Equations, IMPA (1969). | Zbl | MR
[24] ) .- Weak solutions of semilinear hyperbolic equations, Anais da Acad. Bras. Ciências 42 n° 4 (1970). | Zbl | MR
[25] ) and ) . - Strong solution and exponential decay for a nonlinear hyperbolic equation, Applicable Analysis 51 (1993), pp. 155-173. | Zbl | MR
[26] ) . - Stability and decay for a class of nonlinear hyperbolic problems, Asymptotic Analysis 1 (1988), pp. 141-185. | Zbl | MR
[27] ) . - Uniform stabilization of the wave equation by nonlinear boundary feedback, SIAM J.Control Optim. 28, n° 2 (1990), pp. 466-477. | Zbl | MR
[28] ) . - Controlabilidad Exact a y Estabilización de la Ecuación de Ondas, Textos de Métodos Matemáticos 23, IM-UFRJ (1992).
Cité par Sources :