This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1--3 for probing discontinuous part conductivity local temperature flow measurements at boundary. The approach based on use complex spherical waves, no knowledge needed about initial distribution. In dimension two we show how conformal transformations can be used deeper than possible discs. Results numerical experiments...

We consider an inverse boundary value problem for the heat equation ∂ t u = div (γ∇ x u) in (0, T) × Ω, f on ∂Ω, u| t=0 0, a bounded domain Ω ⊂ ℝ n , ≥ 2, where conductivity γ(t, x) is piecewise constant and surface of discontinuity depends time: k 2 (x ∈ D(t)), 1 Ω∖D(t)). Fix direction e* 𝕊 n−1 arbitrarily. Assuming that ∂D(t) strictly convex 0 ≤ T, we show sup {e*·x; D(t)} (0 T), particular D(t) itself, are determined from Dirichlet-to-Neumann map : → ∂ν u(t, x)|(0, T)×∂Ω. The knowledge...

We study the inverse problem of simultaneous identification two discontinuous diffusion coefficients for a one-dimensional coupled parabolic system with observation only one component. The stability result is obtained by Carleman-type estimate. Results from numerical experiments in case are reported, suggesting that method makes possible to recover coefficients.

We consider the heat equation with a diffusion coefficient that is discontinuous at an interface. give global Carleman estimates for solutions of this equation, even if jump across interface has not constant sign.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not.The documents may come from teaching institutions in France abroad, public private centers.L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de scientifiques niveau recherche, publiés ou non, émanant des établissements d'enseignement recherche français étrangers, laboratoires publics privés. Uniqueness Hölder...

We consider an inverse boundary value problem for the heat equation on interval $(0,1)$, where conductivity $\gamma(t,x)$ is piecewise constant and point of discontinuity depends time: $\gamma(t,x) = k^2 \ (0 < x s(t))$, 1\ (s(t) 1)$. First, we show that $k$ $s(t)$ time $[0,T]$ are determined from a partial Dirichlet-to-Neumann map: $u(t,1) \to \partial_xu(t,1), 0 t T$, $u(t,x)$ being solution to such $u(t,0)=0$, independently initial data $u(0,x)$. Second, another $u(t,0) $u(t,1)=0$,...

We study the Rellich type theorem (RT) for Maxwell operator $\hat H^D=\hat D\hat H_0$ on ${\bf Z}^3$ with constant anisotropic medium, i.e. permittivity and permeability of which are non-scalar diagonal matrices. also unique continuation perturbed H^{D_p}=\hat {D}_p\hat where locally from a matrix compact set in Z}^3$. It then implies that, if H^D- \lambda$ satisfies (RT), all distributions u$ Besov space $\mathcal B_0^{\ast}({\bf Z}^3;{\bf C}^3)$ satisfying equation $(\hat H^{D_p} -...

Perpignan et le Roussillon ne deviennent terrain de nombreux chantiers d’architecture privée qu’à la fin du XIXe siècle, d’une part en raison des nouveaux besoins représentation commanditaires importants, dans plaine roussillonnaise ou un peu plus loin, à partir années 1890, conséquence prospérité viticole industrielle alors plutôt récente et, d’autre part, ville, par déblocage situation verrouillée les servitudes militaires, 1906. Un assez grand nombre d’importants voient jour, confiés...

par un obstacle en dimension 2

Let 𝒩(μ) be the counting function of eigenvalues associated with self-adjoint operator −∇(ρ(x, z)∇·) in domain Ω = ℝ × ]0, h[, h > 0, Neuman or Dirichlet conditions at z h. If ρ 1 exterior a bounded rectangular region 𝒪, that is, for ∣x∣ large, then is known to sublinear: proof consists spectral analysis quadratic form obtained from Green formula on 𝒪. In our case, medium multistratified: ρ(x, z) satisfies ρ(z) large. Since direct use previous fails, we modify and obtain estimate N(μ) ⩽...

À l’approche de l’année 2014 et sa commémoration programmée la Première Guerre mondiale, Direction générale des patrimoines au sein du Ministère Culture Communication, a demandé collège monuments historiques l’Inspection réfléchir à question protections vestiges témoignages conflit. Rédigé en novembre 2012, ce présent texte est le rapport présenté patrimoines, faisant un bilan, cette date, protection titre patrimoine lié englobant les ruines protégées lendemain conflit, aux morts érigés...

We are interested by the spectral analysis of anisotropic discrete Maxwell operator $\hat H^D$ defined on square lattice $\rm Z\!\!\! Z^3$. In aim to prove that limiting absorption principle holds we construct a conjugate Fourier series at any not-zero real value. addition show some particular thresholds is essentially self-adjoint.

The equation of acoustic oscillations in multistratified waveguides is considered. It assumed that the properties medium do not depend on longitudinal coordinate a neighbourhood infinity and may be different at ends waveguides. proved truncated resolvent corresponding operator admits an analytical continuation through continuous spectrum. singularities (poles, branching points) spectrum are investigated. large time asymptotic behavior compulsory due to periodic forces obtained.