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1 0 0 0 OA On the embedding constant of the Sobolev type inequality for fractional derivatives

著者
Makoto Mizuguchi Akitoshi Takayasu Takayuki Kubo Shin'ichi Oishi
出版者
The Institute of Electronics, Information and Communication Engineers
雑誌
Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)
巻号頁・発行日
vol.7, no.3, pp.386-394, 2016 (Released:2016-07-01)
参考文献数
20
This paper is concerned with the embedding constant of the Sobolev type inequality for fractional derivatives on $\Omega\subset\mathbb{R}^{N}~(N\in\mathbb{N})$. The constant is explicitly described using the analytic semigroup over L2(Ω) generated by the Laplace operator. Some numerical examples of estimating the embedding constant are also provided.

1 0 0 0 OA Inclusion of periodic solutions for forced delay differential equation modeling El Niño

著者
Shin'ichi Oishi Kouta Sekine
出版者
The Institute of Electronics, Information and Communication Engineers
雑誌
Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)
巻号頁・発行日
vol.12, no.3, pp.575-610, 2021 (Released:2021-07-01)
参考文献数
27
A computer assisted proof is presented for the existence of various periodic solutions for forced Suarez-Schopf's equation, which are delay differential equations modeling El Niño. Tight inclusions of periodic solutions are calculated through numerical verification method by utilizing a structure of Galerkin's equation for forced Suarez-Schopf's equation effectively. The existence of various periodic solutions has been proved via computer assisted proofs including various subharmonics. Especially, coexistence of several subharmonics are proved and numerical simulations are presented suggesting an appearance of chaos.