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November 2014 Determination of a nonlinearity from blow-up time
Yutaka Kamimura, Hiroyuki Usami
Proc. Japan Acad. Ser. A Math. Sci. 90(9): 127-132 (November 2014). DOI: 10.3792/pjaa.90.127

Abstract

We study an inverse problem to determine a nonlinearity of an autonomous equation from a blow-up time of solutions of the equation. A local well-posedness of the inverse problem near a nonlinearity of the type $u^{1+\sigma}$, $\sigma>0$, is established. The paper also suggests that the inverse problem has a good, mathematical structure from a viewpoint of the Wiener-Hopf theory in integral equations.

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Yutaka Kamimura. Hiroyuki Usami. "Determination of a nonlinearity from blow-up time." Proc. Japan Acad. Ser. A Math. Sci. 90 (9) 127 - 132, November 2014. https://doi.org/10.3792/pjaa.90.127

Information

Published: November 2014
First available in Project Euclid: 6 November 2014

zbMATH: 1317.34025
MathSciNet: MR3277204
Digital Object Identifier: 10.3792/pjaa.90.127

Subjects:
Primary: 34A55
Secondary: 45G05

Keywords: blow-up time , inverse problem , multiplicative Wiener-Hopf

Rights: Copyright © 2014 The Japan Academy

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Vol.90 • No. 9 • November 2014
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