Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schrödinger equations

Hiroshi Takase

doi:10.3792/PJAA.97.009

Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schrödinger equations

Research output: Contribution to journal › Article › peer-review

Abstract

In 1963, Kumano-go presented one non-uniqueness example for the two-dimensional wave equation with a time-dependent potential. We construct infinitely many non-uniqueness examples with different wave numbers at infinity for Cauchy problems of the two-dimensional wave equation and Schrödinger equation as a generalization of the construction by Kumano-go.

Original language	English
Pages (from-to)	45-50
Number of pages	6
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	97
Issue number	7
DOIs	https://doi.org/10.3792/PJAA.97.009
Publication status	Published - 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.3792/PJAA.97.009

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title = "Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schr{\"o}dinger equations",

abstract = "In 1963, Kumano-go presented one non-uniqueness example for the two-dimensional wave equation with a time-dependent potential. We construct infinitely many non-uniqueness examples with different wave numbers at infinity for Cauchy problems of the two-dimensional wave equation and Schr{\"o}dinger equation as a generalization of the construction by Kumano-go.",

author = "Hiroshi Takase",

note = "Funding Information: This work was supported by Leading Graduate Course for Frontiers of Mathematical Sciences (FMSP) and JSPS KAKENHI Grant Number JP20J11497. Publisher Copyright: {\textcopyright} 2021. The Japan Academy.",

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AB - In 1963, Kumano-go presented one non-uniqueness example for the two-dimensional wave equation with a time-dependent potential. We construct infinitely many non-uniqueness examples with different wave numbers at infinity for Cauchy problems of the two-dimensional wave equation and Schrödinger equation as a generalization of the construction by Kumano-go.

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Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schrödinger equations

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