Arbitrarily slow approach to limiting behavior

K. Golden, S. Goldstein

Research output: Contribution to journalArticlepeer-review

Abstract

Let f(k, t): RN × [0, ∞)→R be jointly continuous in k and t, limt → ∞ f(k, t) = F(k)with discontinuous for a dense set Γ of k's. It is proven that there exists a dense set T of k's such that, for k ∈ Γ, f(k, t) − F(k) approaches 0 arbitrarily slowly, i.e., roughly speaking, more slowly than any expressible function g(t) → 0. This result is applied to diffusion and conduction in quasiperiodic media and yields arbitrarily slow approaches to limiting behavior as time or volume becomes infinite. Such a slow approach is in marked contrast to the power laws widely found for random media, and, in fact, implies that there is no law whatsoever governing the asymptotics.

Original languageEnglish (US)
Pages (from-to)109-119
Number of pages11
JournalProceedings of the American Mathematical Society
Volume112
Issue number1
DOIs
StatePublished - May 1991

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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