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Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 3
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Original Articles

Uniform stabilization of solutions of a nonlinear system of viscoelastic equations

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Pages 247-263 | Received 14 Nov 2006, Accepted 05 Sep 2007, Published online: 19 Mar 2008

References

  • Andrade , D and Mognon , A . 2003 . Global solutions for a system of Klein–Gordon equations with memory . Bol. Soc. Paran. Mate., Ser. 3 , 21 ( 1/2 ) : 127 – 136 .
  • Berrimi , S and Messaoudi , SA . 2004 . Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping . Elect. J. Diff. Eq. , 2004 ( 88 ) : 1 – 10 .
  • Berrimi , S and Messaoudi , SA . 2006 . Existence and decay of solutions of a viscoelastic equation with a localized damping and a nonlinear source . Nonlinear Anal., TMA , 64 : 2314 – 2331 .
  • Cavalcanti , MM . 2001 . Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping . Diff. Integ. Eq. , 14 ( 1 ) : 85 – 116 .
  • Cavalcanti , MM , Domingos Cavalcanti , VN and Ferreira , J . 2001 . Existence and uniform decay for nonlinear viscoelastic equation with strong damping . Math. Methods Appl. Sci. , 24 : 1043 – 1053 .
  • Cavalcanti , MM , Cavalcanti Domingos , VN and Soriano , JA . 2002 . Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping . Elec. J. Diff. Eq. , 2002 ( 44 ) : 1 – 14 .
  • Cavalcanti , MM and Oquendo , HP . 2003 . Frictional versus viscoelastic damping in a semilinear wave equation . SIAM J. Cont. Optim. , 42 ( 4 ) : 1310 – 1324 .
  • Dafermos , CM . 1970 . Asymptotic stability in viscoelasticity . Arch. Ration. Mech. Anal. , 37 : 297 – 308 .
  • Da Silva Ferreira , J . 1994 . Exponential decay of the energy of a nonlinear system of Klein–Gordon equations with localized dampings in bounded and unbounded domains . Asympt. Anal. , 8 : 73 – 92 .
  • Kawashima , S and Shibata , Y . 1992 . Global existence and exponential stability of small solutions to nonlinear viscoelasticity . Commun. Math. Phys. , 148 : 189 – 208 .
  • Kirane , M and Tatar , N-e . 1999 . A memory type boundary stabilization of a mildly damped wave equation . Elec. J. Qual. Theory Diff. Eq. , 6 : 1 – 7 .
  • Li , MR and Tsai , LY . 2003 . Existence and nonexistence of global solutions of some system of semilinear wave equations . Nonlinear Anal., TMA , 54 : 1397 – 1415 .
  • Medeiros , LA and Milla Miranda , M . 1987 . Weak solutions for a system of nonlinear Klein–Gordon equations . Annal. Matem. Pura Appl. , CXLVI : 173 – 183 .
  • Messaoudi , SA and Tatar , N-e . 2003 . Global existence asymptotic behavior for a Nonlinear Viscoelastic Problem . J. Math. Sci. Res. , 7 ( 4 ) : 136 – 149 .
  • Messaoudi , SA . 2003 . Blow up and global existence in a nonlinear viscoelastic wave equation . Math. Nachrich. , 260 : 58 – 66 .
  • Messaoudi , SA . 2006 . Blow up of solutions with positive initial energy in a nonlinear viscoelastic equation . J. Math. Anal. Appl. , 320 : 902 – 915 .
  • Muñoz Rivera , JE , Lapa , EC and Baretto , R . 1996 . Decay rates for viscoelastic plates with memory . J. Elast. , 44 : 61 – 87 .
  • Santos , ML . 2002 . Decay rates for solutions of a system of wave equations with memory . Elect. J. Diff. Eq. , 2002 ( 38 ) : 1 – 17 .
  • Segal , IE . 1963 . The global Cauchy problem for relativistic scalar field with power interactions . Bull. Soc. Math. France , 91 : 129 – 135 .
  • Wu , ST . 2006 . Blow-up of solutions for an integro-differential equation with a nonlinear source . Elect. J. Diff. Eq. , 2006 ( 45 ) : 1 – 9 .
  • Zhang , J . 2003 . On the standing wave in coupled non-linear Klein–Gordon equations . Math. Methods Appl. Sci. , 26 : 11 – 25 .

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