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Israel Journal of Mathematics

, Volume 225, Issue 1, pp 1–33 | Cite as

Well-posedness for mutational equations under a general type of dissipativity conditions

  • Yoshikazu Kobayashi
  • Naoki Tanaka
Article
  • 33 Downloads

Abstract

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, yD r (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.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and EngineeringChuo UniversityTokyoJapan
  2. 2.Department of Mathematics, Faculty of ScienceShizuoka UniversityShizuokaJapan

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