INVERSE PROBLEMS FOR GENERAL PARABOLIC SYSTEMS AND APPLICATION TO ORNSTEIN-UHLENBECK EQUATION

被引：4
|
作者：
Hassi, El Mustapha Ait Ben [1 ]
Chorfi, Salah-Eddine [1 ]
Maniar, Lahcen [1 ]
机构：
[1] Cadi Ayyad Univ, Fac Sci Semlalia, LMDP, UMMISCO IRD UPMC, BP 2390, Marrakech, Morocco
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年 / 17卷 / 5-6期
关键词：
  Inverse problems; observability; abstract parabolic equations; logarith-mic convexity; Ornstein-Uhlenbeck equation; L-P SPACES; NULL-CONTROLLABILITY; INITIAL CONDITIONS; RESPECT; RECONSTRUCTION; INEQUALITIES; STABILITY; OPERATOR;
D O I：
10.3934/dcdss.2022212
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the link between inverse problems and final state observability for a general class of parabolic systems. We generalize a stability result for initial data known for the case of self-adjoint dissipative operators. More precisely, we consider a system governed by an analytic semigroup. Under the assumption of final state observability, we prove a logarithmic stability estimate depending on the analyticity angle of the semigroup. This is done by using a general logarithmic convexity result. The abstract result is illustrated by considering the Ornstein-Uhlenbeck equation.
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页码：1966 / 1980
页数：15
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