2018年4月1日
Well-posedness for mutational equations under a general type of dissipativity conditions
Israel Journal of Mathematics
- ,
- 巻
- 225
- 号
- 1
- 開始ページ
- 1
- 終了ページ
- 33
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s11856-018-1660-x
- 出版者・発行元
- Springer New York LLC
This paper is concerned with mutational analysis found by Aubin and developed by Lorenz. To extend their results so that they can be applied to quasi-linear evolution equations initiated by Kato, we focus on a mutational framework where for each r >
0 there exists M ≥ 1 such that d(ϑ(t, x), ϑ(t, y)) ≤ Md(x, y) for t ∈ [0, 1] and x, y ∈ Dr(φ), where ϑ is a transition and Dr(φ) is the revel set of a proper lower semicontinuous functional φ. The setting that the constant M may be larger than 1 plays an important role in applying to quasi-linear evolution equations. In that case, it is difficult to estimate the distance between two approximate solutions to mutational equations. Our strategy is to construct a family of metrics depending on both time and state, with respect to which transitions are contractive in some sense.
0 there exists M ≥ 1 such that d(ϑ(t, x), ϑ(t, y)) ≤ Md(x, y) for t ∈ [0, 1] and x, y ∈ Dr(φ), where ϑ is a transition and Dr(φ) is the revel set of a proper lower semicontinuous functional φ. The setting that the constant M may be larger than 1 plays an important role in applying to quasi-linear evolution equations. In that case, it is difficult to estimate the distance between two approximate solutions to mutational equations. Our strategy is to construct a family of metrics depending on both time and state, with respect to which transitions are contractive in some sense.
- ID情報
-
- DOI : 10.1007/s11856-018-1660-x
- ISSN : 1565-8511
- ISSN : 0021-2172
- SCOPUS ID : 85047361897