Stability of the unique continuation for the wave operator via Tataru inequality and applications

详细信息    查看全文

• 作者：Roberta Bosi^a ; ^{roberta.bosi@helsinki.fi" class="auth_mail" title="E-mail the corresponding author} ; Yaroslav Kurylev^b ; ^{y.kurylev@ucl.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Matti Lassas^a ; ^{matti.lassas@helsinki.fi" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 35B53 ; 35B60 ; 35L05 ; 58J45 ; 93B05 ; secondary ; 35R30 ; 31B20 ; 58E25
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：260
• 期：8
• 页码：6451-6492
• 全文大小：593 K

文摘

In this paper we study the stability of the unique continuation in the case of the wave equation with variable coefficients independent of time. We prove a logarithmic estimate in an arbitrary domain of Rⁿ⁺¹${\mathbb{R}}^{n+1}$, where all the parameters are calculated explicitly in terms of the C¹$C^1$-norm of the coefficients and on the other geometric properties of the problem. We use the Carleman-type estimate proved by Tataru in 1995 and an iteration of the local stability. We apply the result to the case of a wave equation with data on a cylinder and we get a stable estimate for any positive time, also after the first conjugate point associated with the geodesics of the metric of the variable coefficients.