2. )1 (

3. Cavalcanti 2002 Berrimi and Messaoudi

4. Cavalcanti 2003

5. Cavalcanti 2001

6. damping terms source term Messaoudi and Tatar

7. Messaoudi

8. (A1) (A2) (A3) (A4) (A5) )1 ( Decay of solutions

9. Proposition if Then the solution

10. Decay of solutions 1. 2. Lemmas (2) (3)(5) (4) 3.3.

11. Decay of solutions 4.4. (6)

12. Proof (8) (9)

13. (10) (11)

14. (12) (13)

15. (14) (15)

16. Decay of solutions 5.5. (16)

17. Let be given Assume that (A1)-(A5) hold. Then, for each, there exist strictly positive constants K and, such that the solution of (1) satisfies, for all Theorem

18. Proof (17) (18)

19. (19)

20. (20)

21. (21) (22) (23)

22. Remark 3.1. This result generalizes and improves the results of [1-4]. In particular, it allows some relaxation functions which satisfy Remark 3.3. Estimates (23) is also true for boundedness of by virtue of continuity and Remark 3.2. Note that the exponential and the polynomial decay estimates are only particular cases of (14). More precisely, we obtain exponential decay for instead of and polynomial decay for