Related papers: Inverse Problems For Third-Order Nonlinear Perturb…
We solve an inverse problem for a third order differential operator under the 3-point Dirichlet conditions. The third-order operator is an $L$-operator in the Lax pair for the good Boussinesq equation. We construct the mapping from the set…
We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…
An inverse problem for a nonlinear biharmonic operator is under consideration in the spirit of Isakov (1993) and Johansson-Nurminen-Salo (2023). We prove that a general nonlinear term of the $Q= Q(x,u, \nabla u, \Delta u)$ associated to a…
We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a…
We show that the knowledge of the Dirichlet--to--Neumann map for a nonlinear magnetic Schr\"odinger operator on the boundary of a compact complex manifold, equipped with a K\"ahler metric and admitting sufficiently many global holomorphic…
We consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator $\mathcal L_{g,X,q}$, with $X$ being a $W^{1,\infty}$ vector field and $q$ being an $L^\infty$ function on compact Riemannian…
A third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this operator coincides with the spectrum of the…
In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $\Gamma$ and the eigenvalues corresponding to a set…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary…
We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…
We prove that a continuous potential $q$ can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonic operator $\Delta_g^2+q$ on a conformally transversally anisotropic Riemannian manifold…
In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…
A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…
We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in $\R^n$ with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the…
We study an inverse boundary value problem for a polyharmonic operator in two dimensions. We show that the Cauchy data uniquely determine all the anisotropic perturbations of orders at most $m-1$ and several perturbations of orders $m$ to…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…