Uniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type

  • Marcelo M. Cavalcanti
  • Valéria N. Domingos Cavalcanti
  • Mauro L. Santos
Conference paper
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 166)


In this article we study the hyperbolic problem (1) where Ω is a bounded region in R n whose boundary is partitioned into disjoint sets Γ0, Γ1. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the relaxation function.


wave equation gradient nonlinearity boundary memory term 


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Copyright information

© International Federation for Information Processing 2005

Authors and Affiliations

  • Marcelo M. Cavalcanti
    • 1
  • Valéria N. Domingos Cavalcanti
    • 1
  • Mauro L. Santos
    • 2
  1. 1.Department of MathematicsState University of MaringáMaringá - PRBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal do ParáParáBrazil

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