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Rendiconti del Circolo Matematico di Palermo

, Volume 51, Issue 1, pp 207–212 | Cite as

Asymptotic behavior of solutions to a wave equation with a non linear dissipative term in ℝ n

  • M. Aassila
Article
  • 31 Downloads

Abstract

In this note we investigate the asymptotic behavior of solutions to the wave equation:u"-Δu+g(u')=0 in ℝnxℝ+.

AMS Subject Classification

35B40 35B37 

Key words

asymptotic behavior nonlinear dissipation energy functional 

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References

  1. [1]
    Aassila M.,Nouvelle approche à la stabilisation forte des systèmes distribués, C. R. Acad. Sci. Paris Sér. I Math.,324 (1997), 43–48.MATHMathSciNetGoogle Scholar
  2. [2]
    Aassila M.,A new approach of strong stabilization of distributed systems, Differential and Integral Equations,11 (1998), 369–376.MATHMathSciNetGoogle Scholar
  3. [3]
    Aassila M.,Some remarks on a second order evolution equation, Electronic Journal of Differential Equations,1998 (1998), 1–6.Google Scholar
  4. [4]
    Kawashima S., Nakao M., Ono K.,On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term, J. Math. Soc. Japan,47 (1995), 617–653.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Lions J. L., Strauss W. A.,Some nonlinear evolution equations, Bull. Soc. Math. France93 (1965), 43–96.MATHMathSciNetGoogle Scholar
  6. [6]
    Motai T.,Asymptotic behavior of solutions to the Klein-Gordon equation with a nonlinear dissipative term, Tsukuba J. of Math.,15 (1991), 151–160.MATHMathSciNetGoogle Scholar
  7. [7]
    Nakao M.,Energy decay of the wave equation with a nolinear dissipative term, Funkcial Ekvac,26 (1983), 237–250.MATHMathSciNetGoogle Scholar
  8. [8]
    Strauss W. A.,The energy method in nonlinear partial differential equations, Notas de Matematica, Brasil Inst. Math. Pure e Aplicada, Rio de Janeiro, 1969).Google Scholar

Copyright information

© Springer 2002

Authors and Affiliations

  • M. Aassila
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur et C.N.R.S.Strasbourg CedexFrance

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