Related papers: Identification of time-varying source term in time…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order $\alpha\in(0,2]$ in time. In the first problem, the sources are supposed to move along known…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…
In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei. First, the existence, the positivity and the long time behavior of…
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…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\partial_t^\alpha u(x,t)+\mathcal{A} u(x,t)=f(x)h(t)+g(x) \dot{\mathbb{W}}(t).$$ The interested inverse problem is to…
In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…
We consider a diffusion and a wave equations: $$ \partial_t^ku(x,t) = \Delta u(x,t) + \mu(t)f(x), \quad x\in \Omega, \, t>0, \quad k=1,2 $$ with the zero initial and boundary conditions, where $\Omega \subset \mathbb{R}^d$ is a bounded…
In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and…
In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of…
The Schr\"odinger equation $i \partial_t^\rho u(x,t)-u_{xx}(x,t) = p(t)q(x) + f(x,t)$ ( $0<t\leq T, \, 0<\rho<1$), with the Riemann-Liouville derivative is considered. An inverse problem is investigated in which, along with $u(x,t)$, also a…
This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…