2015/06/12 by Olivier Poisson, Poisson, Olivier
Chemistry · Computer Science · Engineering · Mathematics · #35K05 #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Boundary (topology) #Boundary value problem #Bounded function #Chemistry #Composite Material Mechanics #Dirichlet distribution #Discontinuity (linguistics) #Domain (mathematical analysis) #Elliptic operator #FOS: Mathematics #Mathematical analysis #Mathematics #Nabla symbol #Numerical methods in inverse problems #Omega #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Smoothness #Uniqueness #math.AP #msc:35K05 #msc:35R30
paper · pdf · doi:10.48550/arxiv.1506.03980
arxiv created 2015/06/12 · openalex publication_date 2015/06/12 · arxiv updated 2015/06/15 · openalex created_date 2019/07/30 · openalex updated_date 2026/08/05
We consider an inverse boundary value problem for the heat equation ∂t v = \rm divx (γ∇x v) in (0,T)×Ω, where Ω is a bounded domain of R3, the heat conductivity γ(t,x) admits a surface of discontinuity which depends on time and without any spatial smoothness. The reconstruction and, implicitly, uniqueness of the moving inclusion, from the knowledge of the Dirichlet-to-Neumann operator, is realised by a dynamical probe method based on the construction of fundamental solutions of the elliptic operator -Δ+ τ2⋅, where τ is a large real parameter, and a couple of inequalities relating data and integrals on the inclusion, which are similar to the elliptic case. That these solutions depend not only on the pole of the fundamental solution, but on the large parameter τ also, allows the method to work in the very general situation.