The global existence of nonlinear evolutionary equation with small delay

We investigate the global existence of the delayed nonlinear evolutionary equation ∂ tu + a u = f (u (t),u (t - τ)). our work space is the fractional powers space x α. under the fundamental theorem on sectorial operators,we make use of the fixed-point principle to prove the local existence and uniqueness theorem. then,the global existence is obtained by gronwall's inequality. © 2012 xunwu yin.