# An observability estimate for parabolic equations from a measurable set in time and its applications

Kim Dang Phung; Gengsheng Wang

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 2, page 681-703
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topPhung, Kim Dang, and Wang, Gengsheng. "An observability estimate for parabolic equations from a measurable set in time and its applications." Journal of the European Mathematical Society 015.2 (2013): 681-703. <http://eudml.org/doc/277408>.

@article{Phung2013,

abstract = {This paper presents a new observability estimate for parabolic equations in $\Omega \times (0,T)$, where $\Omega $ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\Omega $ and a subset of positive measure in $(0,T)$. This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.},

author = {Phung, Kim Dang, Wang, Gengsheng},

journal = {Journal of the European Mathematical Society},

keywords = {parabolic equations; observability estimate; quantitative unique continuation; bang-bang property; nonempty subset of $\Omega $; positive measure in $(0,T)$; time optimal control; convex domain; parabolic equations; observability estimate; quantitative unique continuation; bang-bang property; nonempty subset of ; positive measure in (0,T); bang-bang property for norm; time optimal control; convex domain},

language = {eng},

number = {2},

pages = {681-703},

publisher = {European Mathematical Society Publishing House},

title = {An observability estimate for parabolic equations from a measurable set in time and its applications},

url = {http://eudml.org/doc/277408},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Phung, Kim Dang

AU - Wang, Gengsheng

TI - An observability estimate for parabolic equations from a measurable set in time and its applications

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 2

SP - 681

EP - 703

AB - This paper presents a new observability estimate for parabolic equations in $\Omega \times (0,T)$, where $\Omega $ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\Omega $ and a subset of positive measure in $(0,T)$. This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.

LA - eng

KW - parabolic equations; observability estimate; quantitative unique continuation; bang-bang property; nonempty subset of $\Omega $; positive measure in $(0,T)$; time optimal control; convex domain; parabolic equations; observability estimate; quantitative unique continuation; bang-bang property; nonempty subset of ; positive measure in (0,T); bang-bang property for norm; time optimal control; convex domain

UR - http://eudml.org/doc/277408

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.