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July 2021 Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schrödinger equations
Hiroshi Takase
Proc. Japan Acad. Ser. A Math. Sci. 97(7): 45-50 (July 2021). DOI: 10.3792/pjaa.97.009

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.

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Hiroshi Takase. "Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schrödinger equations." Proc. Japan Acad. Ser. A Math. Sci. 97 (7) 45 - 50, July 2021. https://doi.org/10.3792/pjaa.97.009

Information

Published: July 2021
First available in Project Euclid: 21 July 2021

Digital Object Identifier: 10.3792/pjaa.97.009

Subjects:
Primary: 35A02
Secondary: 35L05 , 35Q41

Keywords: Cauchy problems for partial differential equations , Non-uniqueness for Cauchy problems , unique continuation

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 7 • July 2021
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