Geodesic
Decay estimates of solutions of a nonlinearly damped semilinear wave equation
Aissa Guesmia1 ; Salim A. Messaoudi2
1Département de Mathématiques UFR MIM, Université de Metz Ile de Saulcy 57045 Metz, France
2Mathematical Sciences Department KFUPM Dhahran 31261, Saudi Arabia
Annales Polonici Mathematici, Tome 85 (2005) no. 1, pp. 25-36
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap85-1-3
Keywords: consider initial boundary value problem equation mit delta u nabla phi cdot nabla first prove local global existence results under suitable conditions weak solutions decay either algebraically exponentially depending rate growth result improves includes earlier decay results established authors

Aissa Guesmia  1   ; Salim A. Messaoudi  2

1 Département de Mathématiques UFR MIM, Université de Metz Ile de Saulcy 57045 Metz, France
2 Mathematical Sciences Department KFUPM Dhahran 31261, Saudi Arabia 
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Aissa Guesmia; Salim A. Messaoudi. Decay estimates of solutions of a nonlinearly
 damped semilinear wave equation. Annales Polonici Mathematici, Tome 85 (2005) no. 1, pp. 25-36. doi: 10.4064/ap85-1-3

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