Exponential decay of non-linear wave equation with a viscoelastic boundary condition

Mathematical Methods in the Applied Sciences

Volumn 23, Issue 1, 2000, Pages 41-61

  Rivera, Jaime E Muñoz ^a   Andrade, Doherty ^b  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b STATE UNIVERSITY OF MARINGÁ   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; INTEGRAL EQUATIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; ONE DIMENSIONAL; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

EXPONENTIAL DECAY; NONLINEAR WAVE EQUATION; RELAXATION FUNCTION; VISCOELASTIC BOUNDARY CONDITION;

WAVE EQUATIONS;

EID: 0343789613     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(20000110)23:1<41::AID-MMA102>3.0.CO;2-B     Document Type: Article

References (16)

1. Ciarletta, M., 'A differential problem for heat equation with a boundary condition with memory', Appl. Math. Lett., 10(1), 95-101 (1997).
2. Dafermos, C. M., 'On the existence and the asymptotic stability of solution to the equation of linear thermoelastic', Arch. Rat. Mech. Anal., 29, (1968) 241-271.
3. Fabrizio, M., and Morro, A., 'A boundary condition with memory in Electromagnetism', Arch. Rational Mech. Anal., 136, 359-381 (1996).
4. Greenberg, J. M. and Li Ta-Tsien, 'The effect of boundary damping for the quasilinear wave equation', J. Differential Equations, (52), 66-75 (1984).
5. Horn, M. A. and Lasiecka, I., 'Uniform decay of weak solutions to a Von Karman plate with nonlinear boundary dissipation', Differential Integral Equations, 7(4), 885-908 (1994).
6. Komornik, V., 'Rapid boundary stabilization of the wave equation', SIAM J. Control Optim., 29, 197-208 (1991).
7. Komornik, V. and Zuazua, E., 'A direct method for the boundary stabilization of the wave equation', J. Math. Pures Appl. 69, 33-54 (1990).
8. Lasiecka, I., 'Global uniform decay rates for the solution to the wave equation with nonlinear boundary conditions', Appl. Anal., 47, 191-212 (1992).
9. Lasiecka, I., 'Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation ocurring in the moments only', J. Differential Equations, 95, 169-182 (1992).
10. Σ', Bolle. U.M.I., 7, 665-702 (1991).
11. Muñoz Rivera, J. E., 'Global smooth solution and uniform rate of decay in nonlinear viscoelastic', Rev. Math. Phys., 6(5), 855-868 (1994).
12. Ono, K., 'A stretched string equation with a boundary dissipation', Kyushu J. Math., 28, 265-281 (1994).
13. Qin, T., 'Global solvability of nonlinear wave equation with a viscoelastic boundary condition, Chin. Ann. Math., 14B(3), 335-346 (1993).
14. Qin, T., 'Breakdown of solutions to nonlinear wave equation with a viscoelastic boundary condition', Arab. J. Sci. Engng., 19(2A), 195-201 (1994).
15. Weixi, S. and Songmu, Z., 'Global smooth solution to the system of one dimensional thermoelasticity with dissipation boundary condition', Chin. Ann. Math. Ser. B, 7, 303-317 (1986).
16. Zuazua, E., 'Uniform stabilization of the wave equation by nonlinear boundary feedback', SIAM J. Control Optim., 28, 466-477, (1990).