Inverse problems for general parabolic systems and application to Ornstein-Uhlenbeck equation

2021/10/04 by El Mustapha Ait Ben Hassi, Hassi, E. M. Ait Ben, S. E. Chorfi +3 · 1 citation
Computer Science · Engineering · Mathematics · #35K65 #35K90 #35R30 #93B07 #93C25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2110.01321

openalex publication_date 2021/10/04 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

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 due to García and Takahashi [16], 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.

Citations

• Properties of solutions of ordinary differential equations in banach space

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• Logarithmic convexity of evolution equations and application to inverse problems

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