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Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 3-4: Approximation Theory and Signal Analysis, a special issue in honour of Professor Paul Leo Butzer
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Original Articles

Local asymptotic stability for polyharmonic Kirchhoff systems†

G. Autuori Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
&
P. Pucci Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, ItalyCorrespondence[email protected]
Pages 493-514 | Received 08 Mar 2010, Accepted 01 Apr 2010, Published online: 16 Sep 2010

References

  • Zhu , X . 2001 . Decay rate of solutions of a wave equation with damping and external force . Nonlinear Anal. , 46 : 335 – 345 .
  • Santos , ML , Rocha , MPC , Pereira , DC and Ferreira , J . 2005 . Solvability for a nonlinear coupled system of Kirchhoff type for the beam equations with nonlocal boundary conditions . Electron. J. Qual. Theory Differ. Equ. , 6 : 1 – 28 .
  • Peradze , J . 2009 . A numerical algorithm for a Kirchhoff-type nonlinear static beam . J. Appl. Math. , Art. ID 818269, (12 pages)
  • Autuori , G , Pucci , P and Salvatori , MC . 2009 . Asymptotic stability for nonlinear Kirchhoff systems . Nonlinear Anal. Real World Appl. , 10 : 889 – 909 .
  • Pucci , P and Serrin , J . 1998 . Local asymptotic stability for dissipative wave systems . Israel J. Math. , 104 : 29 – 50 .
  • Autuori , G , Pucci , P and Salvatori , MC . 2009 . Asymptotic stability for anisotropic Kirchhoff systems . J. Math. Anal. Appl. , 352 : 149 – 165 .
  • Autuori , G . 2010 . Kirchhoff systems: Asymptotic stability, global nonexistence and blow up , Ph.D. Thesis University of Firenze .
  • Nakao , M . 2009 . An attractor for a nonlinear dissipative wave equation of Kirchhoff type . J. Math. Anal. Appl. , 353 : 652 – 659 .
  • Pucci , P and Serrin , J . 1993 . Precise damping conditions for global asymptotic stability of second order systems . Acta Math. , 170 : 275 – 307 .
  • Pucci , P and Serrin , J . 1996 . Asymptotic stability for non-autonomous dissipative wave systems . Comm. Pure Appl. Math. , 49 : 177 – 216 .
  • Adams , RA and Fournier , JJF . 2003 . “ Sobolev Spaces ” . In Pure and Applied Mathematics, , 2nd , Vol. 140 , Amsterdam : Academic Press .
  • Boccuto , A and Filippucci , R . 1998 . On the eigenvalues of the polyharmonic operator. Dedicated to Prof. C. Vinti . Atti Sem. Mat. Fis. Univ. Modena , 46 : 479 – 496 .
  • Autuori , G and Pucci , P . Asymptotic stability for Kirchhoff Systems in variable exponent Sobolev spaces , submitted for publication
  • Ziemer , WP . 1989 . “ Weakly Differentiable Functions ” . In Graduate Text in Mathematics , Vol. 120 , New York : Springer-Verlag .

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