On a hyperbolic coefficient inverse problem via partial dynamic boundary measurements.
On a quasilinear inverse boundary value problem.
On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
In this paper, a nonlinear backward heat problem with time-dependent coefficient in the unbounded domain is investigated. A modified regularization method is established to solve it. New error estimates for the regularized solution are given under some assumptions on the exact solution.
On an inverse problem for a linear hyperbolic integrodifferential equation.
On determination of two time-dependent coefficients in a parabolic equation.
On determining a riemannian manifold from the Dirichlet-to-Neumann map
On global behavior of solutions to an inverse problem for semi-linear hyperbolic equations.
On non-overdetermined inverse scattering at zero energy in three dimensions
We develop the -approach to inverse scattering at zero energy in dimensions of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction of the Faddeev generalized scattering amplitude in the...
On the backward heat problem: evaluation of the norm of .
On the backward parabolic equation: a critical survey of some current methods
On the behavior of a nonstationary Poiseuille solution as .
On the distributional solution of the inverse problem induced by the heat kernel method.
On the inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation with constant coefficients of the second order
On the mathematical basis of the linear sampling method.
On the problem of determining the parameters of a layered elastic medium and an impulse source.
On the problem of determining the structure of a layered medium and the shape of an impulse source.
On the solution of inverse problems for generalized oxygen consumption
We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.
On the solution of some inverse problems in infiltration
In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA....
On the solution of some inverse problems in porous media flow.
On the variational principles for partial differential equations