2024-03-28T11:46:28Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00040293
2022-12-19T04:15:35Z
312:6865:7047:7048
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The Cauchy-Kovalevsky Theorem and Noncompactness Measures
Ghisi, Marina
138890
415
application/pdf
We give an abstract version of the Cauchy-Kovalevsky Theorem for the equation $ u' = A(t,u)$ where $A $ is a Caratheodory operator having properties based on noncompactness measures, including Lipschitz and compactness conditions. We give an application of this result to the equation $\partial_{t}^n u + \sum_{i=1,n} f_{i}(u)B^{(n - i + 1)} \partial_{t}^{i - 1}u = 0$ that generalizes the Kirchhoff equation for the vibrating string, when $B$ is {\em not} a compact operator. Our technique is based on Nagumo's weights and on Tonelli delayed problems.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
1997
application/pdf
Journal of mathematical sciences, the University of Tokyo
3
4
627
647
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40293/files/jms040307.pdf
eng