数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (S1): 25-30.
李刚1, Jong Kyu Kim2
Li Gang1, Jong Kyu Kim2
摘要: This paper dwells upon the asymptotic behavior, as t→∞, of the integral solution u(t) to the nonhaear evolution equation u'(t) ∈A(t)u(t) + g(t),t ≥ s,u(s)=x0∈D(A(a)),where {A(t)}t ≥ s is a family m-disipative operator in a Hlilbert space H,and g∈Lloc(0,∞;H). We prove that σ(t,h)=1/t-x∫xtu(θ+h)dθ converges weakly, as t→∞, uniforluly in h ≥ 0, which applies that u(t) is weak convergence if and only if u(t) is weakly asymptotically regular i.e., u(t + h) -u(t) →0 for h ≥ 0.