Control and inverse problems for the heat equation with strong singularities
Avdonin S. Avdonina N. Edward J. Nurtazina K.
February 2021Elsevier B.V.
Systems and Control Letters
2021#148
We consider a linear system composed of N+1 one dimensional heat equations connected by point-mass-like interface conditions. Assume an L2 Dirichlet boundary control at one end, and Dirichlet boundary condition on the other end. Given any L2-type initial temperature distribution, we show that the system is null controllable in arbitrarily small time. The proof uses known results for exact controllability for the associated wave equation. An argument using the Fourier Method reduces the control problem for both the heat equation and the wave equation to certain moment problems. Controllability is then proved by relating minimality properties of the family of exponential functions associated to the wave with the family associated to the heat equation. Based on the controllability result we solve the dynamical inverse problem, i.e. recover unknown parameters of the system from the Dirichlet-to-Neumann map given at a boundary point.
Heat equation , Inverse problem , Null controllability , Strong singularities
Text of the article Перейти на текст статьи
Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, 99775, AK, United States
Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russian Federation
Department of Mathematics and Statistics, Florida International University, Miami, 33199, FL, United States
L.N.Gumilyov Eurasian National University, 2 Satpayev Str., Nur Sultan, 010008, Kazakhstan
Department of Mathematics and Statistics
Moscow Center for Fundamental and Applied Mathematics
Department of Mathematics and Statistics
L.N.Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026