相关论文: Simultaneous determination of coefficients, intern…

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…

Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…

This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing…

In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…

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…

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…

We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…

In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1.…

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

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…

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…

In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…

This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…

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…

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.

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…