Fast decay of solutions for wave equations with localized dissipation on noncompact Riemannian manifolds

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• 作者：Zhifei Zhang ^{zhangzf@hust.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Wave equation on Riemannian manifolds ; Localized dissipation ; Fast energy decay ; Wave equation with variable coefficient ; Exterior domain
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：27
• 期：Complete
• 页码：246-260
• 全文大小：663 K

文摘

In this paper, uniform energy and L² decay for solutions of linear wave equations with an energy term and localized dissipation on certain noncompact Riemannian manifolds are considered. We prove that the total energy of the solutions decay like O(1/t²) as t goes to infinity under some assumptions on the curvature of the manifolds and initial data. It is shown that the decay depends not only on the initial data but also on the curvature properties of the manifolds. As an application, we obtain the decay rate for the solutions of the wave equation with variable coefficients on an exterior domain of Rⁿ.