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.
References
Cannarsa P., Da Prato G., Zolesio J.,The damped wave equation in a moving domain, J. Diff. Equations,85 (1990), 1–16.
Ebihara Y.,On some nonlinear evolution equations with strong dissipation, J. Diff. Equations,30 (1978), 149–164.
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.
Leoni G.,Asymptotic stability for perturbed Hamiltonian systems, II, Ann. Scuola Norm. Sup. Pisa,23 (1996), 531–549.
Levine H., Serrin J.,Global nonexistence theorems for quasilinear evolution equations with dissipation, Arch. Rational Mach. Anal.,137 (1997), 341–361.
Lindqvist P.,On the equation div(|∇u|p−2∇u)+λ|u|p−2 u=0, Proc. Am. Math. Soc.,109 (1990), 157–164.
Marcati P.,Decay and stability for nonlinear hyperbolic equations, J. Diff. Equations,55 (1984), 30–58.
Marcati P.,Stability for second order abstract evolution equations, Nonlinear Anal.,18 (1984), 237–252.
Nakao M.,Asymptotic stability for some nonlinear evolution equations of second order with unbounded dissipative terms, J. Diff. Equations,30 (1978), 54–63.
Nakao M.,A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan,30 (1978), 747–762.
Pucci P., Serrin J.,Remark on the first eigenspace for polyharmonic operators, Atti Sem. Mat. Fis. Univ. Modena,36 (1988), 107–117.
Pucci P., Serrin J.,Critical exponents and critical dimensions for polyharmonic operators, J. Math. Pures et Appl.,69 (1990), 55–83.
Pucci P., Serrin J.,Precise damping conditions for global asymptotic stability for nonlinear second order systems, Acta Mathematica,170 (1993), 275–307.
Pucci P., Serrin J.,Asymptotic stability for non-autonomous dissipative wave systems, Comm. Pure Appl. Math.,XLIX (1996), 177–216.
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.
Pucci P., Serrin J.,Local asymptotic stability for dissipative wave systems, Israel J. Math., 1997.
Strauss W. A.,On continuity of functions with values in various Banach spaces, Pacific J. Math.,19, (1966), 543–551.
Webb G.,Existence and asymptotic behavior for a strongly damped nonlinear wave equation, Canad. J. Math.,32 (1980), 631–643.
Zhu X., Ph. D. Thesis, University of Minnesota (1996).
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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
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DOI: https://doi.org/10.1007/BF02844720