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

## TL;DR

This paper establishes a strong unique continuation property for second order hyperbolic equations with time-independent coefficients, showing that flatness on a segment implies local vanishing of solutions.

## Contribution

It proves a novel strong unique continuation result for hyperbolic equations with variable coefficients, extending previous understanding of solution behavior.

## Key findings

- Solutions flat on a segment vanish nearby
- Unique continuation holds for second order hyperbolic equations
- Results apply to equations with variable coefficients

## Abstract

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