arXiv subjects

M. I. Ismailov

Publications and source records attributed to M. I. Ismailov.

2 recordsLinked to original sources

arXiv2024

Boundary null controllability of the heat equation with Wentzell boundary condition and Dirichlet control

We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the system within the framework of boundary control systems, proving its well-posedness. Then we reduce the question to a moment problem. Using the spectral analysis of the associated Sturm-Liouville problem and the moment method, we establish the null controllability of the system at any positive time $T$. Finally, we approximate minimum energy controls by a penalized HUM approach. This allows us to validate the theoretical controllability results obtained by the moment method.

math.OC↗

arXiv2016

Inverse source problem for a time-fractional heat equation with generalized impedance boundary condition

The paper considers an inverse source problem for a one-dimensional time-fractional heat equation with the generalized impedance boundary condition. The inverse problem is the time dependent source parameter identification together with the temperature distrubution from the energy measurement. The well-posedness of the inverse problem is shown by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition and by using the results on Volterra type integral equation with the kernel may have a diagonal singularity.

math.AP↗