Nonlinear boundary stabilization of the wave equations with variable coefficients and time dependent delay

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• 作者：Zhen-Hu Ning^a ; ^{nzh41034@163.com" class="auth_mail} ; Chang-Xiang Shen^a ; Xiaopeng Zhao^b ; Hao Li^c ; Changsong Lin^c ; Yanmei Zhang^d
• 关键词：Wave equations ; Time dependent delay ; Nonlinear boundary feedback ; Riemannian geometry methods
• 刊名：Applied Mathematics and Computation
• 出版年：1 April, 2014
• 年：2014
• 卷：232
• 期：Complete
• 页码：511-520
• 全文大小：382 K

文摘

We study the stabilization the wave equations with variable coefficients in a bounded domain and nonlinear boundary feedback with time dependent delay. By the Riemannian geometry methods and a suitable assumption of delay, we obtain the exponential decay when the nonlinear terms are linearly bounded and a general decay when the nonlinear terms have no upper growth bound.