In this paper we consider an inverse coefficients problem for a quasilinear elliptic equation of divergence form ∇ · C(x, ∇u(x)) = 0, in a bounded smooth domain Ω. We assume that p) around p = 0. We give a reconstruction method for γ and b from the Dirichlet to Neumann map defined on ∂Ω.

We study the inverse problem of determining the vector and scalar potentials A(t, x) = (A0, A1, · · · , An) and q(t, x), respectively, in the relativistic Schrödinger equationwhere Ω is a C 2 bounded domain in R n for n ≥ 3 and T > diam(Ω) from partial data on the boundary ∂Q. We prove the unique determination of these potentials modulo a natural gauge invariance for the vector field term.

In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension n ⩾ 2. In particular we consider the so called interior determination problem. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear wave equation with a time independent potential. For any small solution u = u(t, x) of our non-linear wave equation which is the perturbation of linear wave equation with time-independent potential perturbed by a divergence with respect to (t, x) of a vector whose components are quadratics with respect to ∇ t,x u(t, x). By ignoring the terms with smallness O(|∇ t,x u(t, x)|3), we will show that we can uniquely determine the potential and the coefficients of these quadratics by many boundary measurements at the boundary of the spacial domain over finite time interval and the final overdetermination at t = T. In other words, our measurement is given by the so-called the input-output map (see ()).

In this article we study the inverse problem of determining the convection term and the time-dependent density coefficient appearing in the convection-diffusion equation. We prove the unique determination of these coefficients from the knowledge of solution measured on a subset of the boundary.

It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. As a by-product, we prove that the wave field cannot be real-analytic on each corner point lying on the convex hull of the scatterer. Our arguments are based on the Schwarz reflection principle for the Helmholtz equation satisfying the impedance boundary condition on a flat boundary.