Skip to main content
Log in

Asymptotic stability for abstract evolution equations and applications to partial differential systems

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

Scopo del lavoro è di studiare la stabilità asintotica per le soluzioni di problemi di evoluzione astratti. Si considerano operatori differenziali quali ilp-Laplaciano, e il poliarmonico, termini smorzanti e fortemente smorzanti, potenziali di richiamo o di sorgente.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Cannarsa P., Da Prato G., Zolesio J.,The damped wave equation in a moving domain, J. Diff. Equations,85 (1990), 1–16.

    Article  MATH  Google Scholar 

  2. Ebihara Y.,On some nonlinear evolution equations with strong dissipation, J. Diff. Equations,30 (1978), 149–164.

    Article  MATH  MathSciNet  Google Scholar 

  3. Haraux A.,Recent results on semilinear hyperbolic problems in bounded domains, inPartial Differential Equations, Lecture Notes in Math.,1324, 118–126, Springer-Verlag, Berlin-New York, 1988.

    Chapter  Google Scholar 

  4. Leoni G.,Asymptotic stability for perturbed Hamiltonian systems, II, Ann. Scuola Norm. Sup. Pisa,23 (1996), 531–549.

    MATH  MathSciNet  Google Scholar 

  5. Levine H., Serrin J.,Global nonexistence theorems for quasilinear evolution equations with dissipation, Arch. Rational Mach. Anal.,137 (1997), 341–361.

    Article  MATH  MathSciNet  Google Scholar 

  6. Lindqvist P.,On the equation div(|∇u|p−2u)+λ|u|p−2 u=0, Proc. Am. Math. Soc.,109 (1990), 157–164.

    Article  MATH  MathSciNet  Google Scholar 

  7. Marcati P.,Decay and stability for nonlinear hyperbolic equations, J. Diff. Equations,55 (1984), 30–58.

    Article  MATH  MathSciNet  Google Scholar 

  8. Marcati P.,Stability for second order abstract evolution equations, Nonlinear Anal.,18 (1984), 237–252.

    Article  MathSciNet  Google Scholar 

  9. Nakao M.,Asymptotic stability for some nonlinear evolution equations of second order with unbounded dissipative terms, J. Diff. Equations,30 (1978), 54–63.

    Article  MATH  MathSciNet  Google Scholar 

  10. Nakao M.,A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan,30 (1978), 747–762.

    Article  MATH  MathSciNet  Google Scholar 

  11. Pucci P., Serrin J.,Remark on the first eigenspace for polyharmonic operators, Atti Sem. Mat. Fis. Univ. Modena,36 (1988), 107–117.

    MATH  MathSciNet  Google Scholar 

  12. Pucci P., Serrin J.,Critical exponents and critical dimensions for polyharmonic operators, J. Math. Pures et Appl.,69 (1990), 55–83.

    MATH  MathSciNet  Google Scholar 

  13. Pucci P., Serrin J.,Precise damping conditions for global asymptotic stability for nonlinear second order systems, Acta Mathematica,170 (1993), 275–307.

    Article  MATH  MathSciNet  Google Scholar 

  14. Pucci P., Serrin J.,Asymptotic stability for non-autonomous dissipative wave systems, Comm. Pure Appl. Math.,XLIX (1996), 177–216.

    Article  MathSciNet  Google Scholar 

  15. Pucci P., Serrin J.,Stability for abstract evolution equations, inPartial Differential Equations and Applications, edited by P. Marcellini, G. Talenti and E. Vesentini, pp. 279–288, M. Dekker, New York, 1996.

    Google Scholar 

  16. Pucci P., Serrin J.,Local asymptotic stability for dissipative wave systems, Israel J. Math., 1997.

  17. Strauss W. A.,On continuity of functions with values in various Banach spaces, Pacific J. Math.,19, (1966), 543–551.

    MATH  MathSciNet  Google Scholar 

  18. Webb G.,Existence and asymptotic behavior for a strongly damped nonlinear wave equation, Canad. J. Math.,32 (1980), 631–643.

    MATH  MathSciNet  Google Scholar 

  19. Zhu X., Ph. D. Thesis, University of Minnesota (1996).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boccuto, A., Vitillaro, E. Asymptotic stability for abstract evolution equations and applications to partial differential systems. Rend. Circ. Mat. Palermo 47, 25–48 (1998). https://doi.org/10.1007/BF02844720

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02844720

Keywords

Navigation