A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities (2022)

Lu, S., Salo, M., & Xu, B. (2022). Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities. Inverse Problems, 38(6), Article 065009. https://doi.org/10.1088/1361-6420/ac637a

JYU-tekijät tai -toimittajat

Salo, Mikko

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Lu, Shuai; Salo, Mikko; Xu, Boxi

Lehti tai sarja: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Julkaisuvuosi: 2022

Ilmestymispäivä: 02.04.2022

Volyymi: 38

Lehden numero: 6

Artikkelinumero: 065009

Kustantaja: IOP Publishing

Julkaisumaa: Britannia

Julkaisun kieli: englanti

DOI: https://doi.org/10.1088/1361-6420/ac637a

Julkaisun avoin saatavuus: Ei avoin

Julkaisukanavan avoin saatavuus: 

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/80493

Rinnakkaistallenteen verkko-osoite (pre-print): https://arxiv.org/abs/2111.13446

Tiivistelmä

We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schrödinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearity in solving the inverse Schrödinger potential problem. Noticing that both linearization approaches can be numerically approximated, we provide several reconstruction algorithms for the quadratic and general power type nonlinearity terms, where one of these algorithms is designed based on boundary measurements of multiple wavenumbers. Several numerical examples shed light on the efficiency of our proposed algorithms.

YSO-asiasanat: inversio-ongelmat; osittaisdifferentiaaliyhtälöt

Vapaat asiasanat: increasing stability; inverse Schrödinger potential problem; power type nonlinearities; reconstruction algorithms

Liittyvät organisaatiot

Hankkeet, joissa julkaisu on tehty

OKM-raportointi: Kyllä

Raportointivuosi: 2022

JUFO-taso: 2