Decay estimates of solutions of a nonlinearly damped semilinear wave equation

Tom 85 / 2005

Aissa Guesmia, Salim A. Messaoudi Annales Polonici Mathematici 85 (2005), 25-36 MSC: 35B40, 35L55, 35B37. DOI: 10.4064/ap85-1-3


We consider an initial boundary value problem for the equation $u_{tt}-{\mit \Delta } u-\nabla \phi \cdot \nabla u+f(u)+g(u_{t})=0$. We first prove local and global existence results under suitable conditions on $f$ and $g$. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of $g$. This result improves and includes earlier decay results established by the authors.


  • Aissa GuesmiaDépartement de Mathématiques
    UFR MIM, Université de Metz
    Ile de Saulcy
    57045 Metz, France
  • Salim A. MessaoudiMathematical Sciences Department
    Dhahran 31261, Saudi Arabia

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