Stability analysis of the zero solution for two class evolution equations

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• 作者：Yicheng Liu ; Zhixiang Li
• 关键词：Lyapunov functionals ; Zero solution ; Asymptotically stable ; none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4P961XW-3&_mathId=mml1&_user=1067359&_cdi=5659&_rdoc=15&_acct=C000050221&_ve
• 刊名：Nonlinear Analysis
• 出版年：2008
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：1 October 2008
• 卷：69
• 期：7
• 页码：2058-2076
• 文件大小：349 K

摘要

By constructing some suitable Lyapunov-type functionals and applying the theory of the definite-quadratic form, we obtain the stability of the zero solution of two classes of evolution equations with delays, including reaction–diffusion equations and damped wave equations. Our criteria depend on the derivatives of delays. Consequently, when the delays are constants, these criteria are independent of the magnitudes of the delays, so the delays are harmless for the stability of the zero solution.