Observability from measurable sets for a parabolic equation involving the Grushin operator and applications
Author(s) -
Liu Hanbing,
Zhang Can
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4266
Subject(s) - observability , mathematics , parabolic partial differential equation , norm (philosophy) , operator (biology) , mathematical analysis , work (physics) , partial differential equation , mechanical engineering , biochemistry , chemistry , repressor , political science , transcription factor , law , gene , engineering
In this work, we utilize the existing Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, together with the telescoping series method, to establish an observability inequality from measurable subsets in time‐space variable for the parabolic equation with Grushin operator in some multidimension domains. We can apply this observability inequality to show the bang–bang property for both time optimal and norm optimal control problems for this kind of singular parabolic equation. Copyright © 2016 John Wiley & Sons, Ltd.