The Global Existence of Nonlinear Evolutionary Equation with Small Delay

Abstract EN

We investigate the global existence of the delayed nonlinear evolutionary equation ∂tu+Au=f(u(t),u(t−τ)).

Our work space is the fractional powers space Xα.

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.