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.
Citation
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
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