Inverse Problems for Ultrahyperbolic Schr\"odinger Equations
Fikret G\"olgeleyen, \"Ozlem Kaytmaz
TL;DR
This paper develops a Carleman estimate for ultrahyperbolic Schrödinger equations and proves Hölder stability for inverse problems involving coefficient or source term identification using boundary data.
Contribution
It introduces a novel Carleman estimate and establishes stability results for inverse problems in ultrahyperbolic Schrödinger equations.
Findings
Established a global Carleman estimate for the ultrahyperbolic Schrödinger equation.
Proved Hölder stability for inverse coefficient and source term problems.
Demonstrated the effectiveness of boundary data in solving inverse problems.
Abstract
In this paper, we establish a global Carleman estimate for an Ultrahyperbolic Schr\"odinger equation. Moreover, we prove H\"older stability for the inverse problem of determining a coefficient or a source term in the Ultrahyperbolic Schr\"odinger equation by some lateral boundary data.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Physics Problems · Advanced Mathematical Modeling in Engineering