Decay estimates to equilibrium for some asymptotically autonomous semilinear evolution equations

Article type: Research Article

Authors: Ben Hassen, Imen

Affiliations: Département de Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna, Bizerte, Tunisia. E-mail: imen_benhassen@yahoo.fr

Abstract: We estimate the rate of decay of the difference between a solution and its limiting equilibrium for the nonautonomous first-order problem u˙+ℳu=g(t),  t∈R+ , and for the second-order problem u¨+u˙+ℳu=g(t),  t∈R+, where ℳ is a gradient operator and g is a function which tends to 0 when t tends to ∞.

Keywords: convergence, rate of decay, analytic nonlinearity, nonautonomous, evolution equation

DOI: 10.3233/ASY-2010-0994

Journal: Asymptotic Analysis, vol. 69, no. 1-2, pp. 31-44, 2010