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When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…

Analysis of PDEs · Mathematics 2018-04-04 Gang Bao , Guanghui Hu , Yavar Kian , Tao Yin

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

Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…

Analysis of PDEs · Mathematics 2025-05-06 Hany Gerges , Jaan Janno

This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…

Analysis of PDEs · Mathematics 2025-01-16 Julieta Bollati , Ernesto A. Borrego Rodriguez , Adriana C. Briozzo , Colin Rogers

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

Numerical Analysis · Mathematics 2025-10-24 Kai Yu , Zhiyuan Li , Yikan Liu

This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our case, the inverse problem consists in restoring the…

Analysis of PDEs · Mathematics 2025-05-20 R. R. Ashurov , O. T. Mukhiddinova

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

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…

Numerical Analysis · Mathematics 2026-04-28 Guanqiu Ma , Hongxia Guo , Guanghui Hu

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…

Analysis of PDEs · Mathematics 2019-01-11 Giovanni Covi

In recent years, much attention has been paid to the study of forward and inverse problems for the Rayleigh-Stokes equation in connection with the importance of this equation for applications. This equation plays an important role, in…

Analysis of PDEs · Mathematics 2023-03-21 Ravshan Ashurov , Oqila Mukhiddinova

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

Analysis of PDEs · Mathematics 2026-04-14 Qiling Gu , Wenlong Zhang , Zhidong Zhang

We consider an inverse problem of determining a coefficient $p(x)$ of an evolution equation $\sigma\ppp_tu = a(x)\ppp_x^2u - p(x)u$ for $0<x<\ell$ and $0<t<T$, where $\sigma \in \C \setminus \{0\}$, $\ell>0$ and $T>0$ are arbitrarily given.…

Analysis of PDEs · Mathematics 2024-10-01 Oleg Y , Imanuvilov , Masahiro Yamamoto

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one…

Analysis of PDEs · Mathematics 2022-06-28 Nasser Al-Salti , Erkinjon Karimov

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

This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…

Analysis of PDEs · Mathematics 2026-03-03 Ravshan Ashurov , Damir Shamuratov

In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…

Analysis of PDEs · Mathematics 2024-03-19 Siyu Cen , Bangti Jin , Yavar Kian , Eric Soccorsi , Rachid Zarouf , Zhi Zhou

We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes…

Optimization and Control · Mathematics 2019-05-22 J. G. Caputo , A. Hamdi , A. Knippel

In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…

Analysis of PDEs · Mathematics 2019-04-05 M. S. Salakhitdinov , E. T. Karimov

A fractal mobile-immobile (MIM in short) solute transport model in porous media is set forth, and an inverse problem of determining the fractional orders by the additional measurements at one interior point is investigated by Laplace…

Numerical Analysis · Mathematics 2021-11-29 Gongsheng Li , Xianzheng Jia , Wenyi Liu , Zhiyuan Li