arXiv subjects

Jaan Janno

Publications and source records attributed to Jaan Janno.

5 recordsLinked to original sources

arXiv2026

Uniqueness of simultaneous reconstruction of general space- and time-dependent sources and initial states in fractional diffusion equations and systems from single boundary measurements

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 boundary of the space domain is considered. Uniqueness for this problem is proved under the assumption that an order of a fractional derivative involved in the equation is irrational. The uniqueness result is generalized to an inverse problem for a coupled system of fractional diffusion equations, where both sources and initial states are unknown and first component of the state is measured on the boundary.

math.AP↗

arXiv2025

Inverse problem to determine simultaneously several scalar parameters and a time-dependent source term in a superdiffusion equation involving a multiterm fractional Laplacian

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 over the time is considered. Uniqueness of a solution is proved. The proof uses asymptotics of poles of the Laplace transform of a measured function.

math.AP↗

arXiv2024

Inverse problems for a generalized fractional diffusion equation with unknown history

Inverse problems for a diffusion equation containing a generalized fractional derivative are studied. The equation holds in a time interval $(0,T)$ and it is assumed that a state $u$ (solution of diffusion equation) and a source $f$ are known for $t\in (t_0,T)$ where $t_0$ is some number in $(0,T)$. Provided that $f$ satisfies certain restrictions, it is proved that product of a kernel of the derivative with an elliptic operator as well as the history of $f$ for $t\in (0,t_0)$ are uniquely recovered. In case of less restrictions on $f$ the uniqueness of the kernel and the history of $f$ is shown. Moreover, in a case when a functional of $u$ for $t\in (t_0,T)$ is given the uniqueness of the kernel is proved under unknown history of $f$.

math-ph↗

arXiv2022

Inverse source problem with a posteriori boundary measurement for fractional diffusion equations

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 of space or time dependent source terms. We prove also the unique determination of a general class of space-time dependent separated variables source terms from such measurement. Our approach is based on the study of singularities of the Laplace transform in time of boundary traces of solutions of time-fractional diffusion equations.

math.AP↗

arXiv2016

Uniqueness for an inverse problem for a semilinear time-fractional diffusion equation

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 of the inverse problem is studied. The method uses a positivity principle of the corresponding differential equation that is also proved in the paper.

math.AP↗