Strong unique continuation for second order hyperbolic equations with time independent coefficients

Abstract

In this paper we prove that if $u$ is a solution to second order hyperbolic equation ${\partial }_t^{2}u+a(x){\partial }_{t}u-(di{v}_x\left(A(x){\nabla }_{x}u\right)+b(x)\cdot {\nabla }_{x}u+c(x)u)=0$ and $u$ is flat on a segment $\{x_0\}\times (-T,T)$ then $u$ vanishes in a neighborhood of $\{x_0\}\times (-T,T)$.

References in corpus (3)

• The stability for the Cauchy problem for elliptic equations
• Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
• Stability Estimates for an Inverse Hyperbolic Initial Boundary Value Problem with Unknown Boundaries