Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation

Authors

  • Eleni Bisognin Departamento de Matemática, Centro de Ciências Naturais e Exatas - CCNE Universidade Federal de Santa Maria - UFSM, Santa Maria, RS.

DOI:

https://doi.org/10.5902/2179460X26355

Abstract

In this work study the existence of global solutions and exponential decay of energy of the mixed problem for perturbed Kirchhoff-Carrier wave equation

u" - M(a(u)) Δu + F(u) + γ u’ = f

where F is a Lipschitz function.

Downloads

Download data is not yet available.

References

AROSIO, A; GARA VALDI, S - On the Degenerate Kirchhoff String, Math. Appl. Science 14 (1991), p. 177-195.

AROSIO, A; SPAGNOLO, S; Global Solutions to the Cauchy Problem for a Nonlinear Hyperbolic Equation, Nonlinear Partial Differential Equations and Their Applications, Collége de France Seminar, vol 6, edited by H. Brezis and J.L. Lions, Pitman (1984).

BERNSTEIN, S - Sur Une Classe d'Equations Fonctionelles Aux Derivées Partielles, Izv Acad. Nauk. SSSR, Ser. Math A, (1940). p. 17-26.

BRlTO, E.H - Decay Estimates for the Generalized Damped Extensible String and Beam Equation. Nonlinear Analysis 8, (1984), p. 1489 - 1496.

CARRIER, G. F - On the Vibration Problem of Elastic String. Q. J. Appl.Math. 3, (1945), p. 151 - 165.

HARAUX, A; ZUAZUA, E - Decay Estimates for Some Semilinear Damped Hyperbolic Problem, Arch. For Rational Mechanics and Analysis, V. 100 N. 2, (1988), p. 191 - 206.

HOSOY A, P; YAMADA, Y - On Some Nonlinear Wave Equations II - Global Existense and Energy Decay of Solutions - to Appear.

KIRCHOFF, G - Vorselungen Über Mechanik Tauber, Leipzig (1883).

LIONS, J.L - On Some Questions in Boundary Value Problem of Mathematica! Phisics, in Contemporary Development in Continuous Mechanics and Partial Differential Equations (Ed. G. de Ia Penha - L.A. Medeiros) North Holland, (1978), London.

LIONS, J. L - MAGENES, E. - Problèrnes Aux Limites Non Homogènes et Applications, Vol 1 , Dunod , Paris, (1968).

MEDEIROS, L. A - MILLA MIRANDA, M - On a Nonlinear Wave Equation With Dampirng Revista Matematica de Ia Universidad Complutense de Madrid, Vol 3, N 2y 3 (1990), p. 213- 23l.

MEDEIROS, L.A - MULA MlRANDA, M - Solution for the Equation of Nonlinear Vibration in Sobolev Spaces of Fractionary Order, Mat. Aplic. Comp. Vo16. N.3, (1987), p. 257 - 276.

MIZOHATA - The Theory of Partial Differential Equations - Cambridge Univ. Press (1973).

NAKAO, M - Decay of Solutions of Some Nonlinear Evolution Equation, Journal of Math. Ann and Appl. 60, (1977), p. 542 - 549.

NAKAO, M - Convergence of Solution of the Wave Equation with Nonlinear Dissipative Term to the Steady State. Mem. Fae; Sei. Kyushi University 30, (1976), p. 257 - 265.

NISHIARA, K - On Global Solution of Some Quasilinear Hyperbolic Equation, Tokyo, J. Math. 7, (1984), p. 437 - 459.

Published

1993-12-13

How to Cite

Bisognin, E. (1993). Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation. Ciência E Natura, 15(15), 17–34. https://doi.org/10.5902/2179460X26355