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2012 The Global Existence of Nonlinear Evolutionary Equation with Small Delay
Xunwu Yin
J. Appl. Math. 2012(SI03): 1-10 (2012). DOI: 10.1155/2012/257140

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.

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Xunwu Yin. "The Global Existence of Nonlinear Evolutionary Equation with Small Delay." J. Appl. Math. 2012 (SI03) 1 - 10, 2012. https://doi.org/10.1155/2012/257140

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1251.34013
MathSciNet: MR2959982
Digital Object Identifier: 10.1155/2012/257140

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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