<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We consider a control problem for one-dimensional heat equation with quadratic cost functional. We prove the existence and uniqueness of a control function from a prescribed set, and study the structure of the set of accessible temperature functions. We also prove the dense controllability of the problem for some set of control functions.</p></abstract>

We consider a control problem for one-dimensional heat equation with quadratic cost functional. We prove the existence and uniqueness of a control function from a prescribed set, and study the structure of the set of accessible temperature functions. We also prove the dense controllability of the problem for some set of control functions.

On The Dense Controllability for The Parabolic Problem with Time-Distributed Functional

Plekhanov Russian University of Economics

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider a control problem for one-dimensional heat equation with quadratic cost functional. We prove the existence and uniqueness of a control function...

On The Dense Controllability for The Parabolic Problem with Time-Distributed Functional

Published Online: Jan 25, 2019

Page range: 9 - 25

Received: Dec 11, 2017

DOI: https://doi.org/10.2478/tmmp-2018-0002

Keywords
heat equation, quadratic cost functional, extremal problem, exact controllability, dense controllability

© 2018 Irina V. Astashova et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On The Dense Controllability for The Parabolic Problem with Time-Distributed Functional

Published Online: Jan 25, 2019

Page range: 9 - 25

Received: Dec 11, 2017

DOI: https://doi.org/10.2478/tmmp-2018-0002

Keywordsheat equation, quadratic cost functional, extremal problem, exact controllability, dense controllability

© 2018 Irina V. Astashova et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
heat equation, quadratic cost functional, extremal problem, exact controllability, dense controllability