Determination of a nonlinearity from blow-up time. (English) Zbl 1317.34025

Kamimura, Yutaka; Usami, Hiroyuki

Proc. Japan Acad., Ser. A 90, No. 9, 127-132 (2014).

Summary: 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.

MSC:

34A55	Inverse problems involving ordinary differential equations
45G05	Singular nonlinear integral equations

Keywords:

inverse problem; blow-up time; multiplicative Wiener-Hopf; autonomous equation

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