Blow-up of solutions to a p-laplace equation

Yuliya Gorb, Alexei Novikov

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field E blows up in the L∞-norm as δ, the distance between the conductors, tends to zero. We give here a concise rigorous justification of the rate of this blow-up in terms of δ. If the current-electric field relation is linear, see similar results obtained earlier in [E. S. Bao, Y. Y. Li, and B. Yin, Arch. Ration. Mech. Anal., 193 (2009), pp. 195-226; H. Kang, M. Lim, and K. H. Yun, preprint, http://arxiv.org/abs/1105.4328v1, 2011; M. Lim and K. Yun, Comm. Partial Differential Equations, 34 (2009), pp. 1287-1315; K. Yun, SIAM J. Appl. Math., 67 (2007), pp. 714-730; K. Yun, J. Math. Anal. Appl., 350 (2009), pp. 306-312].

Original languageEnglish (US)
Pages (from-to)727-743
Number of pages17
JournalMultiscale Modeling and Simulation
Volume10
Issue number3
DOIs
StatePublished - Oct 8 2012

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

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