Open AccessIncreasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data
Author(s) -
Liang Li
Publication year - 2015
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2015.9.469
Subject(s) - initial value problem , stability (learning theory) , cauchy problem , cauchy distribution , mathematics , inverse problem , schrödinger equation , mathematical analysis , inverse , omega , physics , computer science , quantum mechanics , geometry , machine learning
Click on the DOI link to access the article at the publisher's website.To show increasing stability in the problem of recovering potential c is an element of C-1 (Omega) in the Schrodinger 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.NSF grant DMS 10-08902