Polynomial stability of solutions for a system of non-linear viscoelastic equations

References

• Aassila , M , Cavalcanti , MM and Soriano , JA . 2000 . Asymptotic stability and energy decay rates for solutions of the wave equation with memory in star-shaped domains . SIAM J. Contr. Optim. , 38 ( 5 ) : 1581 – 1602 .
   Web of Science ®Google Scholar
• Andrade , D and Mangon , A . 2003 . Global solutions for a system of Klein–Gordon equations with memory . Bol. Soc. Paran. Mate. Ser. 3 , 21 ( 1/2 ) : 127 – 136 .
   Google Scholar
• Berrimi , S and Messaoudi , SA . 2004 . Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping . Electr. J. Diff. Eqns. , 88 : 1 – 10 .
   Google Scholar
• Berrimi , S and Messaoudi , SA . 2006 . Existence and decay of solutions of a viscoelastic equation with a nonlinear source . Nonlinear Anal. TMA , 64 : 2314 – 2331 .
   Web of Science ®Google Scholar
• Barreto , R , Lapa , EC and Munoz Rivera , JE . 1996 . Uniform rates of decay in nonlinear viscoelasticity for polynomially decaying kernels . Appl. Anal. , 60 : 263 – 283 .
   Google Scholar
• Cavalcanti , MM , Domingos Cavalcanti , VN , Prates , JS and Soriano , JA . 2001 . Existence and uniform decay rates for viscoelastic problems with nonlocal boundary damping . Diff. Integral. Eqns. , 14 ( 1 ) : 85 – 116 .
   Google Scholar
• Cavalcanti , MM , Domingos Cavalcanti , VN and Soriano , JA . 2002 . Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping . Elec. J. Diff. Eqns. , 44 : 1 – 14 .
   Google Scholar
• Cavalcanti , MM and Oquendo , HP . 2003 . Fractional versus viscoelastic damping in a semilinear wave equation . SIAM. J. Contr. Optim. , 42 ( 4 ) : 1310 – 1324 .
   Web of Science ®Google Scholar
• Fabrizio , M and Polidoro , S . 2002 . Asymptotic decay for some differential systems with fading memory . Appl. Anal. , 81 : 1245 – 1264 .
   Google Scholar
• Kawashima , S . 1993 . Global solutions to the equation of viscoelasticity with fading memory . J. Diff. Eqns. , 101 ( 2 ) : 388 – 420 .
   Web of Science ®Google Scholar
• Messaoudi , SA . 2008 . General decay of the solution energy in a viscoelastic equation with a nonlinear source . Nonlinear Anal. TMA , 69 : 2589 – 2598 .
   Web of Science ®Google Scholar
• Messaoudi , SA . 2003 . Blow up and global existence in a nonlinear viscoelastic wave equation . Math. Nach. , 260 : 58 – 66 .
   Web of Science ®Google Scholar
• Messaoudi , SA and Tatar , N-E . 2008 . Uniform stabilization of solutions of a nonlinear system of viscoelastic equations . Appl. Anal. , 87 ( 3 ) : 247 – 263 .
   Web of Science ®Google Scholar
• Messaoudi , SA and Tatar , N-E . 2007 . Global existence and uniform stability of solutions for a quasilinear viscoelastic problem . Math. Method Appl. Sci. , 30 : 665 – 680 .
   Web of Science ®Google Scholar
• Rivera , JEM and Baretto , R . 1996 . Decay rates for viscoelastic plates with memory . J. Elasticity , 44 : 61 – 87 .
   Web of Science ®Google Scholar
• Tatar , N-E . 2008 . Polynomial stability without polynomial decay of the relaxation function . Math. Method Appl. Sci. , 29 : 1519 – 1536 .
   Google Scholar
• Wang , YJ and Wang , YF . 2008 . Exponential energy decay of solutions of viscoelastic wave equations . J. Math. Anal. Appl. , 347 ( 1 ) : 18 – 25 .
   Web of Science ®Google Scholar
• Yu , SQ , Wang , MX and Liu , WJ . Blow up for a Cauchy viscoelastic problem with a nonlinear dissipation of cubic convolution type . Math. Method Appl. Sci. , (in press)
   Web of Science ®Google Scholar