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In this paper, we study the inverse problem of finding a time-dependent multiplier of the right-hand side of a time-fractional one-dimensional diffusion equation with variables coefficients in the case where the usual Cauchy, homogeneous…

Analysis of PDEs · Mathematics 2024-11-15 D. K. Durdiev

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

Analysis of PDEs · Mathematics 2024-12-23 S. G. Pyatkov , O. A. Soldatov

We study inverse boundary problems for third-order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in $\mathbb{R}^n$, where $n\geq 3$. By imposing appropriate assumptions on the nonlinearity, we demonstrate…

Analysis of PDEs · Mathematics 2023-12-14 Sombuddha Bhattacharyya , Katya Krupchyk , Suman Kumar Sahoo , Gunther Uhlmann

In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the…

Analysis of PDEs · Mathematics 2023-06-14 Daurenbek Serikbaev , Michael Ruzhansky , Niyaz Tokmagambetov

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…

Analysis of PDEs · Mathematics 2026-04-10 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of…

Analysis of PDEs · Mathematics 2017-10-11 Atsushi Kawamoto

We consider the inverse boundary value problem for the Schrodinger operator with time-dependent electromagnetic potentials in domains with obstacles. We extend the resuls of the author's works [E1], [E2], [E3] to the case of time-dependent…

Analysis of PDEs · Mathematics 2015-07-06 Gregory Eskin

We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…

Analysis of PDEs · Mathematics 2022-10-11 Shitao Liu , Antonio Pierrottet , Scott Scruggs

We are dealing with possibly degenerate second-order parabolic operators whose coefficients are infinitely differentiable with respect to space variables and only measurable with respect to the time variable. We impose the H\"ormander…

Analysis of PDEs · Mathematics 2013-10-10 N. V. Krylov

In this article, we prove a variety of uniqueness results for ultrahyperbolic equations with general space and time dependent lower order terms. We address the problem of determining uniqueness of solutions from boundary data as well as…

Analysis of PDEs · Mathematics 2024-12-04 Vaibhav Kumar Jena

This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary…

Analysis of PDEs · Mathematics 2017-10-11 Mourad Bellassoued , Ibtissem Ben Aïcha

We consider the linearized electrical impedance tomography problem in two dimensions on the unit disk. By a linearization around constant coefficients and using a trigonometric basis, we calculate the linearized Dirichlet-to-Neumann…

Numerical Analysis · Mathematics 2017-06-08 Stefan Kindermann

We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the H\"older Dirichlet problem are well-posed, for any parabolic operator in divergence…

Analysis of PDEs · Mathematics 2025-10-07 Pablo Hidalgo-Palencia , Cody Hutcheson , Joseph Kasel

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

In this paper, we consider a Cauchy problem for a first-order hyperbolic equation with time-dependent coefficients. Cauchy data are given on a lateral subboundary and we obtain local H\"older stabilities for inverse source and coefficient…

Analysis of PDEs · Mathematics 2025-10-13 Giuseppe Floridia , Hiroshi Takase

In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the…

Analysis of PDEs · Mathematics 2024-11-12 Ru-Yu Lai , Gunther Uhlmann , Lili Yan

In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and…

Analysis of PDEs · Mathematics 2026-05-28 Sombuddha Bhattacharyya , Pranav Kumar

The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and…

Analysis of PDEs · Mathematics 2021-10-05 Michael Ruzhansky , Daurenbek Serikbaev , Niyaz Tokmagambetov , Berikbol T. Torebek

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…

Analysis of PDEs · Mathematics 2020-09-25 W. Rundell , M. Yamamoto

We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial…

Analysis of PDEs · Mathematics 2021-01-21 Li Li