An inverse Stefan problem: identification of boundary value

An Inverse Stefan Problem

Inverse boundary value problem for Maxwell equations

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the boundary. We assume that the inaccessible part of the boundary is either part of a plane, or part of a sphere. This work generalizes the results obtained by Isakov [I] for the Schrödinger equation to Maxwell equations. Introduction. Let Ω ⊂ R be a bound...

An Inverse Boundary-value Problem for Semilinear Elliptic Equations

We show that in dimension two or greater, a certain equivalence class of the scalar coefficient a(x, u) of the semilinear elliptic equation ∆u + a(x, u) = 0 is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient a(x, u) can be determined by the Dirichlet to Neumann map under some additional hypotheses.

An inverse boundary value problem for harmonic differential forms

We show that the full symbol of the Dirichlet to Neumann map of the k-form Laplace’s equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series of the metric at the boundary. This extends the result of Lee and Uhlmann for the case k = 0. The proof avoids the computation of the full symbol by using the calculus of pseudo-differential operators...

Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...