Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data

Li Liang

doi:10.3934/ipi.2015.9.469

Article Contents

2015, Volume 9, Issue 2: 469-478. Doi: 10.3934/ipi.2015.9.469

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Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data

Li Liang^1,

1.
Department of Mathematics, Statistics and Physics, Wichita State University, Wichita, KS 67260

Received: March 31, 2014

Revised: December 31, 2014

Published: April 2015

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Abstract

To show increasing stability in the problem of recovering potential $c \in C^1(\Omega)$ in the Schrödinger equation with the given partial Cauchy data when energy frequency $k$ is growing, we will obtain some bounds for $c$ which can be viewed as an evidence of such phenomenon. The proof uses almost exponential solutions and methods of reflection.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J10, 35Q40, 35E05, 81Q15.

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