We study the asymptotic stability for solutions of the nonlinear damped Kirchhoff system, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force f and the distributed damping Q. Then the results are extended to a more delicate problem involving also an internal dissipation of higher order, the so called strongly damped Kirchhoff system. Finally, the study is further extended to strongly damped Kirchhoff–polyharmonic systems, which model several interesting problems of the Woinowsky–Krieger type.
Asymptotic stability for Nonlinear Kirchhoff Systems / Autuori, Giuseppina; Pucci, Patrizia; Salvatori, Maria Cesarina. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 10/2009:2(2009), pp. 889-909. [10.1016/j.nonrwa.2007.11.011]
Asymptotic stability for Nonlinear Kirchhoff Systems
AUTUORI, GIUSEPPINA;
2009-01-01
Abstract
We study the asymptotic stability for solutions of the nonlinear damped Kirchhoff system, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force f and the distributed damping Q. Then the results are extended to a more delicate problem involving also an internal dissipation of higher order, the so called strongly damped Kirchhoff system. Finally, the study is further extended to strongly damped Kirchhoff–polyharmonic systems, which model several interesting problems of the Woinowsky–Krieger type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
