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



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 D r (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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© 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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