About Decay Of Solution Of The Wave Equation With Dissipation

• Cortés Vega, Luis A. ^[1] ; Santiago Ayala, Yolanda S. ^[2]
  1. [1] Universidad de Antofagasta

     Universidad de Antofagasta

     Antofagasta, Chile

     
  2. [2] Universidad Nacional Mayor de San Marcos

     Universidad Nacional Mayor de San Marcos

     Perú

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 26, Nº. 1, 2007, págs. 37-71
• Idioma: inglés
• DOI: 10.4067/S0716-09172007000100003
• Enlaces
  • Texto completo
• Resumen

  • In this work, we consider the problem of existence of global solutions for a scalar wave equation with dissipation. We also study the asymptotic behaviour in time of the solutions. The method used here is based in nonlinear techniques. Key words: wave equation, evolution model, decay of solution, asymptotic behaviour.

• Referencias bibliográficas
  • Citas [1] F. Conrad and B. Rao - Decay of solutions of wave equations in a star-shaped domain with nonlinear boundary feedback. Asympt....
  • [2] L. Cortés-Vega.- A note on resonant frequencies for a system of elastic wave equations, Int. J. Math. Math. Sci. 64, pp. 3485—3498, (2004).
  • [3] L. Cortés-Vega and Y. Santiago-Ayala, Decaimiento de la ecuación de onda con disipación. PESQUIMAT Revista de la Fac. CC. MM. de la UNMSM....
  • [4] L. Hörmander - Linear Partial Differential Operators, Springer-Verlag, New York, 116, (1976).
  • [5] M. Ikawa - Mixed problems for hyperbolic equations of second order. J. Math. Soc. Japan 20, pp. 580—608, (1968).
  • [6] S. Kesavan - Topics in Functional Analysis and applications. John Wiley & Sons, (1989).
  • [7] J. Lagnese, Deacay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations 50, pp. 163—182,...
  • [8] J. Lagnese and J. L. Lions, Modelling Analysis and Control of thin Plates, Masson, Paris, (1989).
  • [9] I. Lasiecka and R. Triggiani, Control Problems for Systems Described by Partial Differential Equations and Applications, Springer Verlag...
  • [10] I. Lasiecka and G. Avalos, Uniform decay rates of solutions to a structural acoustic model with nonlinear dissipation, Appl. Math Comp....
  • [11] I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Diff. Int. Eq,...
  • [12] I. Lasiecka, Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary, J. Diffetential Equations, 79,...
  • [13] V. Komornik- Exact controllability and stabilization. John Wiley & Sons, (1994).
  • [14] V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. 69, pp. 163-182,...
  • [15] P. Martinez. - Decay of solutions of the wave equation with a local highly degenerate dissipation. Asymptotic Analysis 19, pp. 1—17,...
  • [16] M. Nakao - Decay of solutions of the wave equation with a local degenerate dissipation. Israel J. of Maths 95, pp. 25—42, (1996).
  • [17] A. Pazy - Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York, (1983).
  • [18] Y. Santiago A. - Una aplicación del Lema de Nakao. PESQUIMAT Revista de la Fac. CC. MM. de la UNMSM, Nro. 2, pp. 23—36, (2006).
  • [19] Y. Santiago A. - Decaimiento exponencial de la solución débil de una ecuación de onda no lineal. PESQUIMAT Revista de la Fac. CC. MM....
  • [20] Y. Santiago A. and J. Rivera - Global existence and exponential decay to the wave equation with localized frictional damping. PESQUIMAT...
  • [21] D. Tataru, Boundary controllability for conservative PDEs, Appl. Math. Optim. 3, pp. 257—295, (1995).
  • [22] E. Zuazua - Exponential decay for the semi-linear wave equation with locally distributed damping. Comm. Partial Differential Equations....