2012/05/29 by Carlos Montalto, Montalto, Carlos · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1205.6425
openalex publication_date 2012/05/29 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Let (M,g) be a compact Riemmanian manifold with non-empty boundary. Consider\nthe second order hyperbolic initial-boundary value problem (\δt2 +\nP(x,D))u = 0 in (0,T) x M, u(0,x) = \δt u(0,x) = 0 for x in M, u(t,x) =\nf(t,x) on (0,T) x \δ M; where P(x,D) is a first-order perturbation of the\nLaplace-Beltrami operator on (M,g). Let b and q be the covector field and the\npotential of P(x,D), respectively, in M. We prove H "older type stability\nestimates near generic simple Riemannian metrics for the inverse problem of\nrecovering g, b, and q from the hyperbolic Dirichlet-to-Neumann(DN) map\nassociated, f maps to <\ν,u>g - i<\ν,b>g u|\δ M x [0,T] where v is\nunit conormal to the boundary, modulo a class of transformations that fixed the\nDN map.\n