The Global Existence of Nonlinear Evolutionary Equation with Small Delay

Xunwu Yin

Journal of Applied Mathematics, 2012, vol. 2012, 1-10

Abstract:

We investigate the global existence of the delayed nonlinear evolutionary equation ∂ t u + 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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:257140

DOI: 10.1155/2012/257140

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