Proceedings of the 2017 International Seminar on Artificial Intelligence, Networking and Information Technology (ANIT 2017)

An Observability Inequality On A Kind of Linear Parabolic Equation

Authors
D. Luo, Y. Liu, C. Wang, X. Tan
Corresponding Author
D. Luo
Available Online December 2017.
DOI
https://doi.org/10.2991/anit-17.2018.25How to use a DOI?
Keywords
Nash inequality, Poincare inequality, semilinear parabolic equation, observability estimate
Abstract

In this paper, we study the observability inequality on a kind of linear parabolic equation.To show the observability estimate, we first derive the inequalities about the norms of the solution and its gradient, then reduce a lemma of inequality from a corollary directly[1]. At last, combing these inequalities with Nash inequality and Poincare inequality, we give the proof of the observability estimate.

Copyright
© 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2017 International Seminar on Artificial Intelligence, Networking and Information Technology (ANIT 2017)
Series
Advances in Intelligent Systems Research
Publication Date
December 2017
ISBN
978-94-6252-447-7
ISSN
1951-6851
DOI
https://doi.org/10.2991/anit-17.2018.25How to use a DOI?
Copyright
© 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - D. Luo
AU  - Y. Liu
AU  - C. Wang
AU  - X. Tan
PY  - 2017/12
DA  - 2017/12
TI  - An Observability Inequality On A Kind of Linear Parabolic Equation
BT  - Proceedings of the 2017 International Seminar on Artificial Intelligence, Networking and Information Technology (ANIT 2017)
PB  - Atlantis Press
SP  - 148
EP  - 153
SN  - 1951-6851
UR  - https://doi.org/10.2991/anit-17.2018.25
DO  - https://doi.org/10.2991/anit-17.2018.25
ID  - Luo2017/12
ER  -