Recovery of timedependent coefficient on Riemanian manifold for hyperbolic equations
Abstract
Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we study the inverse boundary value problem of determining a timedependent potential $q$, appearing in the wave equation $\partial_t^2u\Delta_g u+q(t,x)u=0$ in $\bar M=(0,T)\times M$ with $T>0$. Under suitable geometric assumptions we prove global unique determination of $q\in L^\infty(\bar M)$ given the Cauchy data set on the whole boundary $\partial \bar M$, or on certain subsets of $\partial \bar M$. Our problem can be seen as an analogue of the Calderón problem on the Lorentzian manifold $(\bar M, dt^2  g)$.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 arXiv:
 arXiv:1606.07243
 Bibcode:
 2016arXiv160607243K
 Keywords:

 Mathematics  Analysis of PDEs;
 35R30;
 35L05;
 58J45