Related papers: Source Identification Problem for a Nonlinear Subd…
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, 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.
In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing 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…
The strong maximum principle is a remarkable characterization of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
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 these lectures I give an introduction to the time-dependent approach to inverse scattering, that has been developed recently. The aim of this approach is to solve various inverse scattering problems with time-dependent methods that…
We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…
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…
In this paper the inverse problem of determining the fractional orders in mixed-type equations is considered. In one part of the domain the considered equation is the subdiffusion equation with a fractional derivative in the sense of…
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the nonlinear reaction term $f(u)$ in a reaction-diffusion equation from overposed data. These measurements can consist of:…
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 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 consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
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…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
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…
A $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ is used to describe a process of a continuous transition from subdiffusion with parameters $\alpha$ and $D_\alpha$ to subdiffusion with…