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We study an inverse problem involving the unique recovery of several lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of boundary. The…

Analysis of PDEs · Mathematics 2021-11-16 Sombuddha Bhattacharyya , Venkateswaran P. Krishnan , Suman Kumar Sahoo

We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is…

Analysis of PDEs · Mathematics 2015-06-04 Oleg Imanuvilov , Masahiro Yamamoto

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

Analysis of PDEs · Mathematics 2021-01-27 Peter Hintz , Gunther Uhlmann , Jian Zhai

We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially…

Differential Geometry · Mathematics 2025-08-05 Jayson Liu

This paper introduces an operator-theoretic paradigm for solving inverse problems in nonlinear balance laws, shifting the focus from identifying specific functional forms to recovering the input-output actions of the associated flux and…

Analysis of PDEs · Mathematics 2025-10-14 Chaohua Duan , Hongyu Liu , Qingle Meng , Li Wang

We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal observation data $g=u(\cdot,T)$. A monotone operator is…

Numerical Analysis · Mathematics 2026-04-16 Liuying Zhang , Wenlong Zhang , Zhidong Zhang

We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary…

Differential Geometry · Mathematics 2024-10-02 Christian Baer , Werner Ballmann

Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac…

Spectral Theory · Mathematics 2015-06-26 Jonathan Eckhardt , Aleksey Kostenko , Gerald Teschl

We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…

Analysis of PDEs · Mathematics 2018-10-10 Sombuddha Bhattacharyya

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…

Classical Analysis and ODEs · Mathematics 2021-04-15 Alberto Cabada , Javier Iglesias

We present an existence and uniqueness result for weak solutions of Dirichlet boundary value problems governed by a nonlocal operator in divergence form and in the presence of a datum which is assumed to belong only to $L^1(\Omega)$ and to…

Analysis of PDEs · Mathematics 2026-03-12 David Arcoya , Serena Dipierro , Edoardo Proietti Lippi , Caterina Sportelli , Enrico Valdinoci

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…

Functional Analysis · Mathematics 2007-05-23 Jochen Brüning , Matthias Lesch

Direct and inverse scattering problem for an operator with non-local potential is solved in the paper. The method is based on the Riemann boundary value problem on a bundle of three straight lines. Description of scattering problem data is…

Classical Analysis and ODEs · Mathematics 2022-01-27 V. A. Zolotarev

In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a…

K-Theory and Homology · Mathematics 2021-09-02 Xiaoman Chen , Hongzhi Liu , Hang Wang , Guoliang Yu

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…

Analysis of PDEs · Mathematics 2018-09-10 Irene Benedetti , Luisa Malaguti , Valentina Taddei

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…

Analysis of PDEs · Mathematics 2011-06-22 Mikko Salo , Xiao Zhong

We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and…

Analysis of PDEs · Mathematics 2018-06-15 Yavar Kian , Yaroslav Kurylev , Matti Lassas , Lauri Oksanen

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…

Analysis of PDEs · Mathematics 2025-11-20 K. Van Bockstal , K. Khompysh

In this paper we study an equation driven by a nonlocal anisotropic operator with homogeneous Dirichlet boundary conditions. We find at least three non trivial solutions: one positive, one negative and one of unknown sign, using variational…

Analysis of PDEs · Mathematics 2018-10-01 Silvia Frassu

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…

Numerical Analysis · Mathematics 2020-11-03 Loic Cappanera , Gabriela Jaramillo , Cory Ward