English

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

Analysis of PDEs 2020-10-13 v1

Abstract

In this paper we prove that if uu is a solution to second order hyperbolic equation t2u+a(x)tu(divx(A(x)xu)+b(x)xu+c(x)u)=0\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 uu is flat on a segment {x0}×(T,T)\{x_0\}\times (-T,T) then uu vanishes in a neighborhood of {x0}×(T,T)\{x_0\}\times (-T,T).

Keywords

Cite

@article{arxiv.1901.02864,
  title  = {Strong unique continuation for second order hyperbolic equations with time independent coefficients},
  author = {Sergio Vessella},
  journal= {arXiv preprint arXiv:1901.02864},
  year   = {2020}
}
R2 v1 2026-06-23T07:07:21.656Z