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

Phung, 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 -