On the boundedness of global solutions of abstract semilinear parabolic equations

[摘要] In this paper we consider the question of the long time behavior of solutions of the initial value problem for evolution equations of the form du/dt + Au(t) = F(u(t)) in a Banach space where A is the infinitesimal generator of an analytic semigroup and F is a nonlinear function such that the initial value problem possesses nonglobal solutions for some initial data. We give sufficient conditions to ensure that global solutions [on [0,infinity)] are necessarily bounded in a suitable norm. We give several examples of problems to which the abstract result applies. (C) 1997 Academic Press.

[发布日期] 1997-12-15