English

Unique determination of a time-dependent potential for wave equations from partial data

Analysis of PDEs 2015-06-18 v3

Abstract

We consider the inverse problem of determining a time-dependent potential qq, appearing in the wave equation t2uΔu+q(t,x)u=0\partial_t^2u-\Delta u+q(t,x)u=0 in Q=(0,T)×ΩQ=(0,T)\times\Omega with Ω\Omega a C2C^2 bounded domain of Rn\mathbb R^n, n2n\geq2, from partial observations of the solutions on Q\partial Q. We prove global unique determination of a coefficient qL(Q)q\in L^\infty(Q) from these observations.

Cite

@article{arxiv.1505.06498,
  title  = {Unique determination of a time-dependent potential for wave equations from partial data},
  author = {Yavar Kian},
  journal= {arXiv preprint arXiv:1505.06498},
  year   = {2015}
}

Comments

The previous version of the paper arXiv:1406.5734 is now decomposed into two different papers with a new uniqueness result (that improves the previous one with weaker conditions and extension to the case of dimension 2) stated in the present paper and a new stability estimate (with different approach than the pervious version and extension to the case of dimension 2) stated in arXiv:1406.5734

R2 v1 2026-06-22T09:40:33.171Z