Related papers: Uniqueness for the inverse boundary value problem …
We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ \epsilon(x)\partial_t u^m-\nabla\cdot\bigl(\gamma(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{in }(0,T)\times\Omega, \] where…
In this paper, a Sturm--Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we…
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…
We consider the Schr\"odinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determined by its scattering amplitude at a fixed positive energy.…
We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…
We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…
We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian.
In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…
Boundary value problem for complete second order elliptic equation is considered in Banach space. The equation and boundary conditions involve a small and spectral parameter. The uniform L_{p}-regularity properties with respect to space…
An initial-boundary value problem for a subdiffusion equation with an elliptic operator $A(D)$ in $\mathbb{R}^N$ is considered. The existence and uniqueness theorems for a solution of this problem are proved by the Fourier method.…
We study the eigenvalues of Schr\"odinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where $V$ decays exponentially at infinity.
In this paper I prove a L^p-L^p' estimate for the solutions of the one-dimensional Schroedinger equation with a potential in L^1_gamma where in the generic case gamma > 3/2 and in the exceptional case (i.e. when there is a half-bound state…
We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…
Let $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and $\Sigma \subset \Omega$ be a compact, $C^2$ submanifold without boundary, of dimension $k$ with $0\leq k < N-2$. Put $L_\mu = \Delta + \mu d_\Sigma^{-2}$ in…
We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…
We study the Robin boundary-value problem for bounded domains with isolated singularities. Because for such domains trace spaces of space $H^1(D)$ on its boundaries are weighted Sobolev spaces $L^{2, \xi}(\partial D)$ existence and…
In this paper, we focus on the inverse scattering problem for the nonlinear Schrodinger equation with magnetic potentials. Specifically, we investigate whether the scattering operator associated with the nonlinear Schrodinger equation can…
We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the…