The Global Existence of Nonlinear Evolutionary Equation with Small Delay

Xunwu Yin

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
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https://doi.org/10.1155/2012/257140

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:257140

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