Inverse source problem and the continuation for a fourth-order parabolic equation in general dimensions

2020/09/24 by Oleg Imanuvilov, Masahiro Yamamoto, Imanuvilov, O. Yu. +1
Mathematics · Computer Science · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2009.11592

Abstract

In this article, for a fourth-order parabolic equation which is closely related for example to the Cahn-Hilliard equation, we study an inverse source problem by interior data and the continuation of solution from lateral Cauchy data. Our method relies on a Carleman estimate and proves conditional stability for both problems.

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