Carleman commutator approach in logarithmic convexity for parabolic equations

2018/02/16 by Kim Dang Phung, Phung, Kim Dang · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1802.05949

openalex publication_date 2018/02/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate on a new strategy combining the logarithmic convexity (or frequency function) and the Carleman commutator to obtain an observation estimate at one time for the heat equation in a bounded domain. We also consider the heat equation with an inverse square potential. Moreover, a spectral inequality for the associated eigenvalue problem is derived.

Cited by

• Logarithmic Convexity and impulse Approximate Controllability for Degenerate Parabolic Equations with Robin Boundary Conditions

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