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In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

Analysis of PDEs · Mathematics 2019-11-14 Suman Kumar Sahoo , Manmohan Vashisth

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

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the…

Analysis of PDEs · Mathematics 2022-08-11 Li Li

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

Analysis of PDEs · Mathematics 2022-03-30 Li Li

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…

Analysis of PDEs · Mathematics 2024-04-17 Anamika Purohit

In this paper we investigate the porous medium equation with a fractional temporal derivative. We justify that the resulting equation emerges when we consider the waiting-time (or trapping) phenomenon that can happen in the medium. Our…

Analysis of PDEs · Mathematics 2015-05-20 Łukasz Płociniczak

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…

Analysis of PDEs · Mathematics 2024-05-03 Rohit Kumar Mishra , Anamika Purohit , Manmohan Vashisth

The main purpose of this article is the study of an inverse problem for nonlocal porous medium equations (NPMEs) with a linear absorption term. More concretely, we show that under certain assumptions on the time-independent coefficients…

Analysis of PDEs · Mathematics 2023-05-26 Yi-Hsuan Lin , Philipp Zimmermann

We study a porous medium equation with right hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator. The derivative in time is also fractional of Caputo-type and which takes into account…

Analysis of PDEs · Mathematics 2015-09-22 Mark Allen , Luis Caffarelli , Alexis Vasseur

This paper explores Barenblatt solutions of the time-fractional porous medium equation, characterized by a Caputo-type time derivative. Employing an integral equation approach, we rigorously prove the existence of these solutions and…

Numerical Analysis · Mathematics 2025-07-28 Josefa Caballero , Hanna Okrasińska-Płociniczak , Łukasz Płociniczak , Kishin Sadarangani

In this work, we consider an inverse problem of determining a time dependent coefficient in a fully fractional diffusion equation with a nonlinear source term. The nonlocal initial-boundary value problem refers to the forward model: the…

Analysis of PDEs · Mathematics 2025-12-10 D. K. Durdiev , H. H. Turdiev

In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…

Analysis of PDEs · Mathematics 2025-08-11 Rahmonov Askar Ahmadovich

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

We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…

Analysis of PDEs · Mathematics 2018-12-05 Yavar Kian , Eric Soccorsi , Masahiro Yamamoto

In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…

Analysis of PDEs · Mathematics 2023-05-02 Ravshan Ashurov , Yusuf Fayziev , Muattar Khudoykulova

This paper explores the forward and inverse problems for a fractional subdiffusion equation characterized by time-dependent diffusion and reaction coefficients. Initially, the forward problem is examined, and its unique solvability is…

Analysis of PDEs · Mathematics 2025-11-10 Ravshan Ashurov , Elbek Husanov

We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…

Analysis of PDEs · Mathematics 2022-04-12 Giovanni Covi , Jesse Railo , Philipp Zimmermann

Many physical, biological, and economical systems exhibit various memory effects due to which their present state depends on the history of the whole evolution. Combined with the nonlinearity of the process these phenomena pose serious…

Numerical Analysis · Mathematics 2022-03-01 Hanna Okrasińska-Płociniczak , Łukasz Płociniczak

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…

Analysis of PDEs · Mathematics 2021-09-09 Li Li
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