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The global existence of nonlinear evolutionary equation with small delay. (English) Zbl 1251.34013
Summary: We investigate the global existence of the delayed nonlinear evolutionary equation \(\partial_t u + Au = f(u(t), u(t - \tau))\) . Our work space is the fractional powers space \(X^a\). 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.
34A08 Fractional ordinary differential equations
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